%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN548+1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:33 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN548+1 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:37:35 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(reachable_type, type, (
% 0.19/0.43 reachable: ( $i * $i ) > $o)).
% 0.19/0.43 tff(tptp_fun_W_3_type, type, (
% 0.19/0.43 tptp_fun_W_3: $i > $i)).
% 0.19/0.43 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.43 tptp_fun_Y_0: $i > $i)).
% 0.19/0.43 tff(initial_world_type, type, (
% 0.19/0.43 initial_world: $i)).
% 0.19/0.43 tff(p_type, type, (
% 0.19/0.43 p: $i > $o)).
% 0.19/0.43 tff(q_type, type, (
% 0.19/0.43 q: $i > $o)).
% 0.19/0.43 tff(tptp_fun_W_4_type, type, (
% 0.19/0.43 tptp_fun_W_4: $i > $i)).
% 0.19/0.43 tff(tptp_fun_Z_1_type, type, (
% 0.19/0.43 tptp_fun_Z_1: $i > $i)).
% 0.19/0.43 tff(tptp_fun_V_2_type, type, (
% 0.19/0.43 tptp_fun_V_2: $i > $i)).
% 0.19/0.43 tff(1,assumption,(~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))), introduced(assumption)).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))) | reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((reachable(X, Y) & reachable(Y, Z)) <=> (~((~reachable(Y, Z)) | (~reachable(X, Y))))), ((~(reachable(X, Y) & reachable(Y, Z))) <=> (~(~((~reachable(Y, Z)) | (~reachable(X, Y))))))), rewrite((~(~((~reachable(Y, Z)) | (~reachable(X, Y))))) <=> ((~reachable(Y, Z)) | (~reachable(X, Y)))), ((~(reachable(X, Y) & reachable(Y, Z))) <=> ((~reachable(Y, Z)) | (~reachable(X, Y))))), (((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> (((~reachable(Y, Z)) | (~reachable(X, Y))) | reachable(X, Z)))), rewrite((((~reachable(Y, Z)) | (~reachable(X, Y))) | reachable(X, Z)) <=> (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))), (((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (^[X: $i, Y: $i, Z: $i] : rewrite(((reachable(X, Y) & reachable(Y, Z)) => reachable(X, Z)) <=> ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : ((reachable(X, Y) & reachable(Y, Z)) => reachable(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.43 tff(12,axiom,(![X: $i, Y: $i, Z: $i] : ((reachable(X, Y) & reachable(Y, Z)) => reachable(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity_of_reachable')).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.43 tff(15,plain,(
% 0.19/0.43 ![X: $i, Y: $i, Z: $i] : ((~(reachable(X, Y) & reachable(Y, Z))) | reachable(X, Z))),
% 0.19/0.43 inference(skolemize,[status(sab)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 ((reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))) <=> ((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[23, 17, 5, 3])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))) | (~q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (~q(tptp_fun_V_2(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[25, 1])).
% 0.19/0.43 tff(27,assumption,(![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))), introduced(assumption)).
% 0.19/0.43 tff(28,assumption,(~q(tptp_fun_V_2(tptp_fun_Y_0(initial_world)))), introduced(assumption)).
% 0.19/0.43 tff(29,assumption,(reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))), introduced(assumption)).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))) | (q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))) <=> ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))) | (q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[32, 29, 28, 27])).
% 0.19/0.43 tff(34,plain,((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[34, 5, 26])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))) | (~p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (~p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[36, 1])).
% 0.19/0.43 tff(38,assumption,(~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))), introduced(assumption)).
% 0.19/0.43 tff(39,assumption,(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), introduced(assumption)).
% 0.19/0.43 tff(40,assumption,(reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))), introduced(assumption)).
% 0.19/0.43 tff(41,assumption,(~p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))), introduced(assumption)).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V))))) <=> ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[44, 41, 40, 39, 38])).
% 0.19/0.43 tff(46,plain,((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), V)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[46, 37, 3, 35])).
% 0.19/0.43 tff(48,assumption,(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))), introduced(assumption)).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | (p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) <=> ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | (p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[51, 41, 40, 48])).
% 0.19/0.43 tff(53,plain,((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[53, 37, 3])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (^[X: $i] : refl(reachable(X, X) <=> reachable(X, X))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (![X: $i] : reachable(X, X) <=> ![X: $i] : reachable(X, X)),
% 0.19/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (![X: $i] : reachable(X, X) <=> ![X: $i] : reachable(X, X)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(58,axiom,(![X: $i] : reachable(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_of_reachable')).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (![X: $i] : reachable(X, X)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.43 tff(60,plain,(
% 0.19/0.43 ![X: $i] : reachable(X, X)),
% 0.19/0.43 inference(skolemize,[status(sab)],[59])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![X: $i] : reachable(X, X)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ((~![X: $i] : reachable(X, X)) | reachable(initial_world, initial_world)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (reachable(initial_world, initial_world)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (^[X: $i] : refl(((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))) <=> ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (^[X: $i] : rewrite(((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))) <=> ![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 ((~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))) <=> (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 ((~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : (reachable(X, Y) => (![Z: $i] : (reachable(Y, Z) => (p(Z) | ![V: $i] : (reachable(Z, V) => q(V)))) <=> (![W: $i] : (reachable(Y, W) => p(W)) | ![W: $i] : (reachable(Y, W) => q(W))))))) <=> (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(77,axiom,(~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : (reachable(X, Y) => (![Z: $i] : (reachable(Y, Z) => (p(Z) | ![V: $i] : (reachable(Z, V) => q(V)))) <=> (![W: $i] : (reachable(Y, W) => p(W)) | ![W: $i] : (reachable(Y, W) => q(W))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (~?[X: $i] : (reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[80, 75])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (^[X: $i] : nnf_neg(refl($oeq((~reachable(initial_world, X)), (~reachable(initial_world, X)))), trans(sk($oeq((~![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))), (~((~reachable(X, tptp_fun_Y_0(X))) | (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))))), nnf_neg(refl($oeq(reachable(X, tptp_fun_Y_0(X)), reachable(X, tptp_fun_Y_0(X)))), nnf_neg(nnf_pos(proof_bind(^[Z: $i] : monotonicity(refl($oeq(p(Z), p(Z))), refl($oeq((~reachable(tptp_fun_Y_0(X), Z)), (~reachable(tptp_fun_Y_0(X), Z)))), nnf_pos(proof_bind(^[V: $i] : refl($oeq((q(V) | (~reachable(Z, V))), (q(V) | (~reachable(Z, V)))))), $oeq(![V: $i] : (q(V) | (~reachable(Z, V))), ![V: $i] : (q(V) | (~reachable(Z, V))))), $oeq((p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))), (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))), $oeq(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))), ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))), trans(sk($oeq((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), (~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(X), V))))))), nnf_neg(refl($oeq((~p(tptp_fun_Z_1(X))), (~p(tptp_fun_Z_1(X))))), refl($oeq(reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)), reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)))), sk($oeq((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(X), V)))), (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))))), $oeq((~(p(tptp_fun_Z_1(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(X), V))))), ((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))), $oeq((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), ((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))))), monotonicity(nnf_pos(proof_bind(^[W: $i] : refl($oeq((p(W) | (~reachable(tptp_fun_Y_0(X), W))), (p(W) | (~reachable(tptp_fun_Y_0(X), W)))))), $oeq(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))), ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))))), nnf_pos(proof_bind(^[W: $i] : refl($oeq((q(W) | (~reachable(tptp_fun_Y_0(X), W))), (q(W) | (~reachable(tptp_fun_Y_0(X), W)))))), $oeq(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))), ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))), $oeq((![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))), (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))))), nnf_neg(sk($oeq((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W)))), (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))))), sk($oeq((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))), (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))), $oeq((~(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))), ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))), $oeq((~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W)))))), ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))), $oeq((~((~reachable(X, tptp_fun_Y_0(X))) | (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))))), (reachable(X, tptp_fun_Y_0(X)) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))), $oeq((~![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W))))))), (reachable(X, tptp_fun_Y_0(X)) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))), $oeq((~(reachable(initial_world, X) & ![Y: $i] : ((~reachable(X, Y)) | (![Z: $i] : (p(Z) | (~reachable(Y, Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) <=> (![W: $i] : (p(W) | (~reachable(Y, W))) | ![W: $i] : (q(W) | (~reachable(Y, W)))))))), ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(83,plain,(
% 0.19/0.44 ![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & ((![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | (![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.44 inference(nnf-neg,[status(sab)],[81, 82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![X: $i] : ((~reachable(initial_world, X)) | (reachable(X, tptp_fun_Y_0(X)) & (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) & (((~p(tptp_fun_Z_1(X))) & reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (~(q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X)))))) | ((~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))))) & (~(q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[83, 74])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[84, 72])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[85, 70])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[86, 65])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 (((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | p(tptp_fun_Z_1(initial_world)) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))) | (~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))))) <=> ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | p(tptp_fun_Z_1(initial_world)) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))) | (~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | p(tptp_fun_Z_1(initial_world)) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))) | (~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | p(tptp_fun_Z_1(initial_world)) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))) | (~(p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, initial_world)) | (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (~((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[93, 87, 63])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))) | reachable(initial_world, tptp_fun_Y_0(initial_world))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 (reachable(initial_world, tptp_fun_Y_0(initial_world))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))))) <=> ((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[102, 87, 96])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))))) | (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.46 tff(106,plain,
% 0.19/0.46 ((~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[107, 54, 47])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 (((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | (q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))) <=> ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | (q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[111, 26, 108, 24])).
% 0.19/0.46 tff(113,plain,((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))))) | ((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 ((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[114, 103])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 ((~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 ((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[117, 113])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 (reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.46 tff(121,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_Y_0(initial_world)), tptp_fun_V_2(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_V_2(tptp_fun_Y_0(initial_world))) | p(tptp_fun_Z_1(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_Z_1(tptp_fun_Y_0(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), W)))))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[121, 103])).
% 0.19/0.46 tff(123,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 ((reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world))))) <=> ((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[125, 123])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Y_0(tptp_fun_Y_0(initial_world)))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[128, 17, 122, 120])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_4(tptp_fun_Y_0(initial_world)))) | q(tptp_fun_W_4(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_Y_0(initial_world)), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world)))) | (~p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (~p(tptp_fun_W_3(tptp_fun_Y_0(initial_world)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[130, 118])).
% 0.19/0.46 tff(132,assumption,(~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))), introduced(assumption)).
% 0.19/0.46 tff(133,assumption,(~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))), introduced(assumption)).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))) | reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[136, 133])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 ((reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))) <=> ((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[139])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[140, 138])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[143, 17, 137, 135])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))) | (~q(tptp_fun_V_2(initial_world)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 (~q(tptp_fun_V_2(initial_world))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[145, 133])).
% 0.19/0.46 tff(147,assumption,(![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))), introduced(assumption)).
% 0.19/0.46 tff(148,assumption,(~q(tptp_fun_V_2(initial_world))), introduced(assumption)).
% 0.19/0.46 tff(149,assumption,(reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))), introduced(assumption)).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 (((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))) <=> ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[152, 149, 148, 147])).
% 0.19/0.46 tff(154,plain,((~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))) | (~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 (~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[154, 137, 146])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))) | (~p(tptp_fun_Z_1(initial_world)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (~p(tptp_fun_Z_1(initial_world))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[156, 133])).
% 0.19/0.46 tff(158,assumption,(~![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))), introduced(assumption)).
% 0.19/0.46 tff(159,assumption,(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))), introduced(assumption)).
% 0.19/0.46 tff(160,assumption,(reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))), introduced(assumption)).
% 0.19/0.46 tff(161,assumption,(~p(tptp_fun_Z_1(initial_world))), introduced(assumption)).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 (((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V))))) <=> ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[164, 161, 160, 159, 158])).
% 0.19/0.47 tff(166,plain,((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_Z_1(initial_world), V)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[166, 157, 135, 155])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 (((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))) | (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[168, 94])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 ((~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W))))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 (![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[171, 167, 132])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))) <=> ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_V_2(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_V_2(initial_world)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[175, 146, 172, 144])).
% 0.19/0.47 tff(177,plain,(((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 ((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[177, 132])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (((~reachable(initial_world, tptp_fun_Y_0(initial_world))) | (~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))))) | ((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 ((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[179, 94])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 ((~((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 ((~((~reachable(tptp_fun_Z_1(initial_world), tptp_fun_V_2(initial_world))) | q(tptp_fun_V_2(initial_world)) | p(tptp_fun_Z_1(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_Z_1(initial_world))))) | (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (~((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[182, 178])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 ((reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world)))) <=> ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(initial_world, tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | (~reachable(initial_world, tptp_fun_Y_0(initial_world))) | reachable(initial_world, tptp_fun_W_3(initial_world))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (reachable(initial_world, tptp_fun_W_3(initial_world))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[191, 17, 96, 185])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))))))) <=> ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(195,plain,
% 0.19/0.47 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W)))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[194])).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 (((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) <=> ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[195, 193])).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | ((~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))) | (~(p(tptp_fun_W_3(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 ((~![X: $i] : ((~reachable(initial_world, X)) | (~((~reachable(X, tptp_fun_Y_0(X))) | (~((~((~reachable(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | p(tptp_fun_Z_1(X)) | q(tptp_fun_V_2(X)) | (~reachable(tptp_fun_Z_1(X), tptp_fun_V_2(X))))) | (~(p(tptp_fun_W_3(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_3(X))) | q(tptp_fun_W_4(X)) | (~reachable(tptp_fun_Y_0(X), tptp_fun_W_4(X))))))) | (~(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(X), W))) | ![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(X), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))))))))) | (~reachable(initial_world, tptp_fun_W_3(initial_world))) | (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (~((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[198, 87, 192])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 (((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W)))))) | ((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 ((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world))) | (~q(tptp_fun_W_4(initial_world)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 (~q(tptp_fun_W_4(initial_world))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[202, 183])).
% 0.19/0.47 tff(204,plain,
% 0.19/0.47 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world))) | reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 (reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[204, 183])).
% 0.19/0.47 tff(206,assumption,(![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))), introduced(assumption)).
% 0.19/0.47 tff(207,assumption,(~q(tptp_fun_W_4(initial_world))), introduced(assumption)).
% 0.19/0.47 tff(208,assumption,(reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))), introduced(assumption)).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 (((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))) <=> ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 ((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[211, 208, 207, 206])).
% 0.19/0.47 tff(213,plain,((~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (~![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[213, 205, 203])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[171, 214, 132])).
% 0.19/0.48 tff(216,plain,
% 0.19/0.48 (((~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_4(initial_world))) | q(tptp_fun_W_4(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | p(tptp_fun_W_3(initial_world))) | (~p(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(217,plain,
% 0.19/0.48 (~p(tptp_fun_W_3(initial_world))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[216, 183])).
% 0.19/0.48 tff(218,plain,
% 0.19/0.48 (((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V))))) <=> ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(219,plain,
% 0.19/0.48 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | (p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 ((~![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(initial_world), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V))))) | p(tptp_fun_W_3(initial_world)) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(initial_world))) | ![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 (![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[220, 185, 217, 215])).
% 0.19/0.48 tff(222,plain,
% 0.19/0.48 (((~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~(![Z: $i] : (p(Z) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), Z)) | ![V: $i] : (q(V) | (~reachable(Z, V)))) | ![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W))) | ![W: $i] : (q(W) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), W)))))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 (reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[222, 199])).
% 0.19/0.48 tff(224,assumption,(~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))), introduced(assumption)).
% 0.19/0.48 tff(225,plain,
% 0.19/0.48 (((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(226,plain,
% 0.19/0.48 (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.19/0.48 tff(227,assumption,(reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))), introduced(assumption)).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 ((reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world))))) <=> ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(230,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[229])).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[230, 228])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[233, 17, 227, 226])).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 (((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))) | (~q(tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 (~q(tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[235, 224])).
% 0.19/0.48 tff(237,assumption,(![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))), introduced(assumption)).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))) <=> ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 (~reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[240, 237, 236])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))) | reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[242, 224])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 ((reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))) <=> ((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[245])).
% 0.19/0.48 tff(247,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[246, 244])).
% 0.19/0.48 tff(248,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(249,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_V_2(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.48 tff(250,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[249, 17, 243, 241, 234])).
% 0.19/0.48 tff(251,plain,(((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | (~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(252,plain,
% 0.19/0.48 ((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[251, 223, 221])).
% 0.19/0.48 tff(253,plain,
% 0.19/0.48 ((~((~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))))) | (~((~reachable(tptp_fun_Z_1(tptp_fun_W_3(initial_world)), tptp_fun_V_2(tptp_fun_W_3(initial_world)))) | q(tptp_fun_V_2(tptp_fun_W_3(initial_world))) | p(tptp_fun_Z_1(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_Z_1(tptp_fun_W_3(initial_world)))))) | (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(254,plain,
% 0.19/0.48 (~((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[253, 252, 201])).
% 0.19/0.48 tff(255,plain,
% 0.19/0.48 (((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | (~q(tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(256,plain,
% 0.19/0.48 (~q(tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.19/0.48 tff(257,plain,
% 0.19/0.48 (((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))) <=> ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(258,plain,
% 0.19/0.48 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | (q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(259,plain,
% 0.19/0.48 ((~![V: $i] : (q(V) | (~reachable(tptp_fun_W_3(initial_world), V)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.19/0.48 tff(260,plain,
% 0.19/0.48 (~reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[259, 221, 256])).
% 0.19/0.48 tff(261,plain,
% 0.19/0.48 (((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | q(tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | p(tptp_fun_W_3(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(262,plain,
% 0.19/0.48 (reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[261, 254])).
% 0.19/0.48 tff(263,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(264,plain,
% 0.19/0.48 ((reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world))))) <=> ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(265,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | ((~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[264])).
% 0.19/0.48 tff(266,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[265, 263])).
% 0.19/0.48 tff(267,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(268,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (reachable(X, Z) | (~reachable(Y, Z)) | (~reachable(X, Y)))) | (~reachable(tptp_fun_Y_0(tptp_fun_W_3(initial_world)), tptp_fun_W_4(tptp_fun_W_3(initial_world)))) | (~reachable(tptp_fun_W_3(initial_world), tptp_fun_Y_0(tptp_fun_W_3(initial_world)))) | reachable(tptp_fun_W_3(initial_world), tptp_fun_W_4(tptp_fun_W_3(initial_world)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.48 tff(269,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[268, 17, 223, 262, 260])).
% 0.19/0.48 tff(270,plain,(![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(271,plain,
% 0.19/0.48 (((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))))) <=> ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(272,plain,
% 0.19/0.48 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | (p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(273,plain,
% 0.19/0.48 ((~![W: $i] : (p(W) | (~reachable(tptp_fun_Y_0(initial_world), W)))) | p(tptp_fun_W_3(tptp_fun_Y_0(initial_world))) | (~reachable(tptp_fun_Y_0(initial_world), tptp_fun_W_3(tptp_fun_Y_0(initial_world))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.19/0.48 tff(274,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[273, 270, 131, 129])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------