%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN941+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:41:02 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN941+1 : TPTP v9.0.0. Released v3.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Fri Jun 20 13:01:39 EDT 2025
% 0.20/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(r_type, type, (
% 0.20/0.38 r: $i > $o)).
% 0.20/0.38 tff(tptp_fun_C_0_type, type, (
% 0.20/0.38 tptp_fun_C_0: $i)).
% 0.20/0.38 tff(tptp_fun_B_1_type, type, (
% 0.20/0.38 tptp_fun_B_1: $i)).
% 0.20/0.38 tff(p_type, type, (
% 0.20/0.38 p: $i > $o)).
% 0.20/0.38 tff(f_type, type, (
% 0.20/0.38 f: $i > $i)).
% 0.20/0.38 tff(q_type, type, (
% 0.20/0.38 q: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : refl(((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))) <=> ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))) <=> ![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) <=> ((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))), ((((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)) <=> (((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0))))))))) & q(X)))), rewrite((((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0))))))))) & q(X)) <=> (~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))), ((((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)) <=> (~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))))), ((~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))) <=> (~(~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))))), rewrite((~(~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))) <=> ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))), ((~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))) <=> ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))) <=> ![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((q(f(B!1)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))) <=> (q(f(B!1)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ((~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))) <=> (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 ((~![B: $i, C: $i] : (q(f(B)) => ?[X: $i, Y: $i] : ((p(f(Y)) => (p(X) & (r(Y) => (r(B) & r(C))))) & q(X)))) <=> (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(8,axiom,(~![B: $i, C: $i] : (q(f(B)) => ?[X: $i, Y: $i] : ((p(f(Y)) => (p(X) & (r(Y) => (r(B) & r(C))))) & q(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (q(f(B!1)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.20/0.38 inference(and_elim,[status(thm)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (q(f(B!1))),
% 0.20/0.38 inference(and_elim,[status(thm)],[13])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (((~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1)))) <=> ((~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[23, 17, 16])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))) | ((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))) | p(f(B!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (p(f(B!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 28, 26])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))) | ((~r(B!1)) | (~r(C!0)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ((~r(B!1)) | (~r(C!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))) | r(B!1)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (r(B!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 ((~((~r(B!1)) | (~r(C!0)))) | (~r(B!1)) | (~r(C!0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (~r(C!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[35, 34, 32])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))) | r(C!0)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[39, 28, 38])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))) | ((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 ((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (((~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1)))) <=> ((~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 17, 16, 42])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------