%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN969+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:41:05 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN969+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 13:06:20 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(p_type, type, (
% 0.12/0.37 p: $i > $o)).
% 0.12/0.37 tff(tptp_fun_B_0_type, type, (
% 0.12/0.37 tptp_fun_B_0: $i)).
% 0.12/0.37 tff(r_type, type, (
% 0.12/0.37 r: $i > $o)).
% 0.12/0.37 tff(q_type, type, (
% 0.12/0.37 q: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0))) <=> ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & ![X: $i] : (q(X) | (~p(X))) & r(B!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((![X: $i] : (q(X) | (~p(X))) & r(B!0)) <=> (![X: $i] : (q(X) | (~p(X))) & r(B!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0))) <=> ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0))) <=> ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & ![X: $i] : (q(X) | (~p(X))) & r(B!0))),
% 0.12/0.37 inference(transitivity,[status(thm)],[3, 1])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))) <=> (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 ((~![B: $i] : ((![X: $i] : (p(X) => q(X)) & r(B)) => (![Y: $i] : (r(Y) => p(Y)) => q(B)))) <=> (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(7,axiom,(~![B: $i] : ((![X: $i] : (p(X) => q(X)) & r(B)) => (![Y: $i] : (r(Y) => p(Y)) => q(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & ![X: $i] : (q(X) | (~p(X))) & r(B!0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (r(B!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (^[Y: $i] : refl((p(Y) | (~r(Y))) <=> (p(Y) | (~r(Y))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![Y: $i] : (p(Y) | (~r(Y))) <=> ![Y: $i] : (p(Y) | (~r(Y)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![Y: $i] : (p(Y) | (~r(Y)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[12])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![Y: $i] : (p(Y) | (~r(Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (((~![Y: $i] : (p(Y) | (~r(Y)))) | (p(B!0) | (~r(B!0)))) <=> ((~![Y: $i] : (p(Y) | (~r(Y)))) | p(B!0) | (~r(B!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((~![Y: $i] : (p(Y) | (~r(Y)))) | (p(B!0) | (~r(B!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((~![Y: $i] : (p(Y) | (~r(Y)))) | p(B!0) | (~r(B!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (p(B!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[20, 17, 13])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (^[X: $i] : refl((q(X) | (~p(X))) <=> (q(X) | (~p(X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![X: $i] : (q(X) | (~p(X))) <=> ![X: $i] : (q(X) | (~p(X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![X: $i] : (q(X) | (~p(X)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[12])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![X: $i] : (q(X) | (~p(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (~q(B!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[12])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (((~![X: $i] : (q(X) | (~p(X)))) | (q(B!0) | (~p(B!0)))) <=> ((~![X: $i] : (q(X) | (~p(X)))) | q(B!0) | (~p(B!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ((~![X: $i] : (q(X) | (~p(X)))) | (q(B!0) | (~p(B!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((~![X: $i] : (q(X) | (~p(X)))) | q(B!0) | (~p(B!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[29, 26, 25, 21])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------