%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN970+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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
% 0.10/0.12 % Problem : SYN970+1 : TPTP v9.0.0. Released v3.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:03:57 EDT 2025
% 0.12/0.33 % 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_A_1_type, type, (
% 0.12/0.37 tptp_fun_A_1: $i)).
% 0.12/0.37 tff(r_type, type, (
% 0.12/0.37 r: $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(elem_2_type, type, (
% 0.12/0.37 elem_2: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : refl((~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X)))))) <=> (~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X)))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X)))))) <=> ![X: $i, Y: $i] : (~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : ?[X: $i, Y: $i] : (r(B) | (~p(A)) | (~(r(Y) | (~p(X)))))) <=> (~![A: $i, B: $i] : ?[X: $i, Y: $i] : (r(B) | (~p(A)) | (~(r(Y) | (~p(X))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((p(X) => r(Y)) => (p(A) => r(B)))) <=> (~![A: $i, B: $i] : ?[X: $i, Y: $i] : (r(B) | (~p(A)) | (~(r(Y) | (~p(X))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((p(X) => r(Y)) => (p(A) => r(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : (r(B) | (~p(A)) | (~(r(Y) | (~p(X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : (r(B) | (~p(A)) | (~(r(Y) | (~p(X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : (r(B) | (~p(A)) | (~(r(Y) | (~p(X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : (r(B) | (~p(A)) | (~(r(Y) | (~p(X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.37 tff(10,plain,(
% 0.12/0.37 $oeq((~?[X: $i, Y: $i] : (r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X)))))), ![X: $i, Y: $i] : (~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X)))))))),
% 0.12/0.37 inference(transitivity,[status(sab)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : (~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X))))))) | (~(r(B!0) | (~p(A!1)) | (~(r(elem!2) | (~p(elem!2))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~(r(B!0) | (~p(A!1)) | (~(r(elem!2) | (~p(elem!2)))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 ((r(B!0) | (~p(A!1)) | (~(r(elem!2) | (~p(elem!2))))) | p(A!1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (p(A!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 ((r(B!0) | (~p(A!1)) | (~(r(elem!2) | (~p(elem!2))))) | (~r(B!0))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (~r(B!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~(r(B!0) | (~p(A!1)))) | r(B!0) | (~p(A!1))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (~(r(B!0) | (~p(A!1)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[18, 17, 15])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((r(B!0) | (~p(A!1)) | (~(r(B!0) | (~p(A!1))))) | (r(B!0) | (~p(A!1)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (r(B!0) | (~p(A!1)) | (~(r(B!0) | (~p(A!1))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : (~(r(B!0) | (~p(A!1)) | (~(r(Y) | (~p(X))))))) | (~(r(B!0) | (~p(A!1)) | (~(r(B!0) | (~p(A!1))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[22, 11, 21])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------