%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN980+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:41:07 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
% 0.00/0.13 % Problem : SYN980+1 : TPTP v9.0.0. Released v3.1.0.
% 0.00/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 13:02:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(p_type, type, (
% 0.20/0.38 p: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_B_0_type, type, (
% 0.20/0.38 tptp_fun_B_0: $i)).
% 0.20/0.38 tff(f_type, type, (
% 0.20/0.38 f: $i > $i)).
% 0.20/0.38 tff(r_type, type, (
% 0.20/0.38 r: $i > $o)).
% 0.20/0.38 tff(q_type, type, (
% 0.20/0.38 q: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,assumption,(~p(f(B!0), B!0)), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[Y: $i] : refl(((~(r(Y) | (~r(B!0)))) | p(f(Y), Y)) <=> ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y)) <=> ![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ((![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y))))) <=> (![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~![B: $i] : ((~![Y: $i] : ((~(r(Y) | (~r(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y))))) <=> (~![B: $i] : ((~![Y: $i] : ((~(r(Y) | (~r(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ((~![B: $i] : (![Y: $i] : ((r(B) => r(Y)) => p(f(Y), Y)) => ?[X: $i, Y: $i] : (p(X, Y) & (q(f(B), B) => q(X, Y))))) <=> (~![B: $i] : ((~![Y: $i] : ((~(r(Y) | (~r(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(7,axiom,(~![B: $i] : (![Y: $i] : ((r(B) => r(Y)) => p(f(Y), Y)) => ?[X: $i, Y: $i] : (p(X, Y) & (q(f(B), B) => q(X, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (~![B: $i] : ((~![Y: $i] : ((~(r(Y) | (~r(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (~![B: $i] : ((~![Y: $i] : ((~(r(Y) | (~r(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~![B: $i] : ((~![Y: $i] : ((~(r(Y) | (~r(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (~![B: $i] : ((~![Y: $i] : ((~(r(Y) | (~r(B)))) | p(f(Y), Y))) | ?[X: $i, Y: $i] : (p(X, Y) & ((~q(f(B), B)) | q(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y)) & ![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))),
% 0.20/0.38 inference(and_elim,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | p(f(B!0), B!0)) <=> ((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | p(f(B!0), B!0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (($false | p(f(B!0), B!0)) <=> p(f(B!0), B!0)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~$true) <=> $false),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((r(B!0) | (~r(B!0))) <=> $true),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~(r(B!0) | (~r(B!0)))) <=> (~$true)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~(r(B!0) | (~r(B!0)))) <=> $false),
% 0.20/0.38 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (((~(r(B!0) | (~r(B!0)))) | p(f(B!0), B!0)) <=> ($false | p(f(B!0), B!0))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (((~(r(B!0) | (~r(B!0)))) | p(f(B!0), B!0)) <=> p(f(B!0), B!0)),
% 0.20/0.38 inference(transitivity,[status(thm)],[21, 16])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | ((~(r(B!0) | (~r(B!0)))) | p(f(B!0), B!0))) <=> ((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | p(f(B!0), B!0))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | ((~(r(B!0) | (~r(B!0)))) | p(f(B!0), B!0))) <=> ((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | p(f(B!0), B!0))),
% 0.20/0.38 inference(transitivity,[status(thm)],[23, 15])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | ((~(r(B!0) | (~r(B!0)))) | p(f(B!0), B!0))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~![Y: $i] : ((~(r(Y) | (~r(B!0)))) | p(f(Y), Y))) | p(f(B!0), B!0)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[26, 14, 1])).
% 0.20/0.38 tff(28,plain,(p(f(B!0), B!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : refl(((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y)))) <=> ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y)))) <=> ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y))) <=> (~((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y)))))), ((~(p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y)))) <=> (~(~((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y)))))))), rewrite((~(~((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y)))))) <=> ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))), ((~(p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y)))) <=> ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y)))) <=> ![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(p(X, Y) & ((~q(f(B!0), B!0)) | q(X, Y))))),
% 0.20/0.38 inference(and_elim,[status(thm)],[12])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | (~p(f(B!0), B!0))) <=> ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | (~p(f(B!0), B!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (((~p(f(B!0), B!0)) | $false) <=> (~p(f(B!0), B!0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (((~q(f(B!0), B!0)) | q(f(B!0), B!0)) <=> $true),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~((~q(f(B!0), B!0)) | q(f(B!0), B!0))) <=> (~$true)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~((~q(f(B!0), B!0)) | q(f(B!0), B!0))) <=> $false),
% 0.20/0.38 inference(transitivity,[status(thm)],[39, 17])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (((~p(f(B!0), B!0)) | (~((~q(f(B!0), B!0)) | q(f(B!0), B!0)))) <=> ((~p(f(B!0), B!0)) | $false)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (((~p(f(B!0), B!0)) | (~((~q(f(B!0), B!0)) | q(f(B!0), B!0)))) <=> (~p(f(B!0), B!0))),
% 0.20/0.38 inference(transitivity,[status(thm)],[41, 37])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | ((~p(f(B!0), B!0)) | (~((~q(f(B!0), B!0)) | q(f(B!0), B!0))))) <=> ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | (~p(f(B!0), B!0)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | ((~p(f(B!0), B!0)) | (~((~q(f(B!0), B!0)) | q(f(B!0), B!0))))) <=> ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | (~p(f(B!0), B!0)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[43, 36])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | ((~p(f(B!0), B!0)) | (~((~q(f(B!0), B!0)) | q(f(B!0), B!0))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~p(X, Y)) | (~((~q(f(B!0), B!0)) | q(X, Y))))) | (~p(f(B!0), B!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[46, 35, 28])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------