%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV664+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n026.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 : Tue May 5 06:56:04 PM UTC 2026
% Result : Theorem 0.74s 0.91s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV664+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.18/0.34 % Computer : n026.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 07:55:25 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.74/0.91 % SZS status Theorem
% 0.74/0.91 % SZS output start Proof
% 0.74/0.91 tff(p_type, type, (
% 0.74/0.91 p: $i > $o)).
% 0.74/0.91 tff(cProp___24t_type, type, (
% 0.74/0.91 cProp___24t: $i > $o)).
% 0.74/0.91 tff(1,plain,
% 0.74/0.91 ((~$true) <=> $false),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(2,plain,
% 0.74/0.91 (![V0__P: $i] : $true <=> $true),
% 0.74/0.91 inference(elim_unused_vars,[status(thm)],[])).
% 0.74/0.91 tff(3,plain,
% 0.74/0.91 (^[V0__P: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[V1__Q: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(V0__P) => p(V1__Q)) <=> (p(V1__Q) | (~p(V0__P)))), (((V0__P = V1__Q) => (p(V0__P) => p(V1__Q))) <=> ((V0__P = V1__Q) => (p(V1__Q) | (~p(V0__P)))))), rewrite(((V0__P = V1__Q) => (p(V1__Q) | (~p(V0__P)))) <=> (p(V1__Q) | (~(V0__P = V1__Q)) | (~p(V0__P)))), (((V0__P = V1__Q) => (p(V0__P) => p(V1__Q))) <=> (p(V1__Q) | (~(V0__P = V1__Q)) | (~p(V0__P))))), ((cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q)))) <=> (cProp___24t(V1__Q) => (p(V1__Q) | (~(V0__P = V1__Q)) | (~p(V0__P)))))), rewrite((cProp___24t(V1__Q) => (p(V1__Q) | (~(V0__P = V1__Q)) | (~p(V0__P)))) <=> (p(V1__Q) | (~(V0__P = V1__Q)) | (~cProp___24t(V1__Q)) | (~p(V0__P)))), ((cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q)))) <=> (p(V1__Q) | (~(V0__P = V1__Q)) | (~cProp___24t(V1__Q)) | (~p(V0__P)))))), (![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q)))) <=> ![V1__Q: $i] : (p(V1__Q) | (~(V0__P = V1__Q)) | (~cProp___24t(V1__Q)) | (~p(V0__P))))), trans(trans(der(![V1__Q: $i] : (p(V1__Q) | (~(V0__P = V1__Q)) | (~cProp___24t(V1__Q)) | (~p(V0__P))) <=> ![V1__Q: $i] : ((~p(V0__P)) | p(V0__P) | (~cProp___24t(V0__P)))), elim_unused(![V1__Q: $i] : ((~p(V0__P)) | p(V0__P) | (~cProp___24t(V0__P))) <=> ((~p(V0__P)) | p(V0__P) | (~cProp___24t(V0__P)))), (![V1__Q: $i] : (p(V1__Q) | (~(V0__P = V1__Q)) | (~cProp___24t(V1__Q)) | (~p(V0__P))) <=> ((~p(V0__P)) | p(V0__P) | (~cProp___24t(V0__P))))), rewrite(((~p(V0__P)) | p(V0__P) | (~cProp___24t(V0__P))) <=> $true), (![V1__Q: $i] : (p(V1__Q) | (~(V0__P = V1__Q)) | (~cProp___24t(V1__Q)) | (~p(V0__P))) <=> $true)), (![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q)))) <=> $true)), ((cProp___24t(V0__P) => ![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q))))) <=> (cProp___24t(V0__P) => $true))), rewrite((cProp___24t(V0__P) => $true) <=> $true), ((cProp___24t(V0__P) => ![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q))))) <=> $true))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(4,plain,
% 0.74/0.91 (![V0__P: $i] : (cProp___24t(V0__P) => ![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q))))) <=> ![V0__P: $i] : $true),
% 0.74/0.91 inference(quant_intro,[status(thm)],[3])).
% 0.74/0.91 tff(5,plain,
% 0.74/0.91 (![V0__P: $i] : (cProp___24t(V0__P) => ![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q))))) <=> $true),
% 0.74/0.91 inference(transitivity,[status(thm)],[4, 2])).
% 0.74/0.91 tff(6,plain,
% 0.74/0.91 ((~![V0__P: $i] : (cProp___24t(V0__P) => ![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q)))))) <=> (~$true)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[5])).
% 0.74/0.91 tff(7,plain,
% 0.74/0.91 ((~![V0__P: $i] : (cProp___24t(V0__P) => ![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q)))))) <=> $false),
% 0.74/0.91 inference(transitivity,[status(thm)],[6, 1])).
% 0.74/0.91 tff(8,axiom,(~![V0__P: $i] : (cProp___24t(V0__P) => ![V1__Q: $i] : (cProp___24t(V1__Q) => ((V0__P = V1__Q) => (p(V0__P) => p(V1__Q)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''_HAMMER_GOAL'')).
% 0.74/0.91 tff(9,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.74/0.91 % SZS output end Proof
% 0.74/0.91 % E exiting
%------------------------------------------------------------------------------