%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM841+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:22:11 AM UTC 2025
% Result : Theorem 0.41s 0.62s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM841+2 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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 02:03:01 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.41/0.62 % SZS status Theorem
% 0.41/0.62 % SZS output start Proof
% 0.41/0.62 tff(vplus_type, type, (
% 0.41/0.62 vplus: ( $i * $i ) > $i)).
% 0.41/0.62 tff(tptp_fun_Vd196_0_type, type, (
% 0.41/0.62 tptp_fun_Vd196_0: ( $i * $i ) > $i)).
% 0.41/0.62 tff(vd345_type, type, (
% 0.41/0.62 vd345: $i)).
% 0.41/0.62 tff(vd344_type, type, (
% 0.41/0.62 vd344: $i)).
% 0.41/0.62 tff(vd348_type, type, (
% 0.41/0.62 vd348: $i)).
% 0.41/0.62 tff(vd347_type, type, (
% 0.41/0.62 vd347: $i)).
% 0.41/0.62 tff(greater_type, type, (
% 0.41/0.62 greater: ( $i * $i ) > $o)).
% 0.41/0.62 tff(1,plain,
% 0.41/0.62 (^[Vd46: $i, Vd47: $i, Vd48: $i] : refl((vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(2,plain,
% 0.41/0.62 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[1])).
% 0.41/0.62 tff(3,plain,
% 0.41/0.62 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(4,axiom,(![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(33, 0), 0)'')).
% 0.41/0.62 tff(5,plain,
% 0.41/0.62 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.41/0.62 tff(6,plain,(
% 0.41/0.62 ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.41/0.62 inference(skolemize,[status(sab)],[5])).
% 0.41/0.62 tff(7,plain,
% 0.41/0.62 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.41/0.62 tff(8,plain,
% 0.41/0.62 ((~![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))) | (vplus(vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vd347, vd348)), tptp_fun_Vd196_0(vd344, vd345)) = vplus(vplus(vd345, vd348), vplus(tptp_fun_Vd196_0(vd347, vd348), tptp_fun_Vd196_0(vd344, vd345))))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(9,plain,
% 0.41/0.62 (vplus(vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vd347, vd348)), tptp_fun_Vd196_0(vd344, vd345)) = vplus(vplus(vd345, vd348), vplus(tptp_fun_Vd196_0(vd347, vd348), tptp_fun_Vd196_0(vd344, vd345)))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.41/0.62 tff(10,plain,
% 0.41/0.62 ((vplus(vd345, vd347) = vplus(vd347, vd345)) <=> (vplus(vd345, vd347) = vplus(vd347, vd345))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(11,axiom,(vplus(vd345, vd347) = vplus(vd347, vd345)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(213, 351, 0)'')).
% 0.41/0.62 tff(12,plain,
% 0.41/0.62 (vplus(vd345, vd347) = vplus(vd347, vd345)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.41/0.62 tff(13,plain,
% 0.41/0.62 (^[Vd193: $i, Vd194: $i] : refl((~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(14,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[13])).
% 0.41/0.62 tff(15,plain,
% 0.41/0.62 (^[Vd193: $i, Vd194: $i] : rewrite((~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(16,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[15])).
% 0.41/0.62 tff(17,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.41/0.62 inference(transitivity,[status(thm)],[16, 14])).
% 0.41/0.62 tff(18,plain,
% 0.41/0.62 (^[Vd193: $i, Vd194: $i] : trans(monotonicity(rewrite((greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))) <=> (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))), ((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))), rewrite((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))), ((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(19,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[18])).
% 0.41/0.62 tff(20,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196))) <=> ![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(21,axiom,(![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''def(cond(conseq(axiom(3)), 11), 1)'')).
% 0.41/0.62 tff(22,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.41/0.62 tff(23,plain,(
% 0.41/0.62 ![Vd193: $i, Vd194: $i] : (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))),
% 0.41/0.62 inference(skolemize,[status(sab)],[22])).
% 0.41/0.62 tff(24,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.41/0.62 tff(25,plain,
% 0.41/0.62 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.41/0.62 tff(26,plain,
% 0.41/0.62 ((~![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))) | (~((~((~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))))) | (~(greater(vd347, vd348) | ![Vd196: $i] : (~(vd347 = vplus(vd348, Vd196)))))))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(27,plain,
% 0.41/0.62 (~((~((~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))))) | (~(greater(vd347, vd348) | ![Vd196: $i] : (~(vd347 = vplus(vd348, Vd196))))))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.41/0.62 tff(28,plain,
% 0.41/0.62 (((~((~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))))) | (~(greater(vd347, vd348) | ![Vd196: $i] : (~(vd347 = vplus(vd348, Vd196)))))) | ((~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))))),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(29,plain,
% 0.41/0.62 ((~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348)))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.41/0.62 tff(30,plain,
% 0.41/0.62 (greater(vd347, vd348) <=> greater(vd347, vd348)),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(31,axiom,(greater(vd347, vd348)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conjunct2(211), 349, 0)'')).
% 0.41/0.62 tff(32,plain,
% 0.41/0.62 (greater(vd347, vd348)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.41/0.62 tff(33,plain,
% 0.41/0.62 ((~((~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))))) | (~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348)))),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(34,plain,
% 0.41/0.62 ((~((~greater(vd347, vd348)) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))))) | (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348)))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.41/0.62 tff(35,plain,
% 0.41/0.62 (vd347 = vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[34, 29])).
% 0.41/0.62 tff(36,plain,
% 0.41/0.62 (vplus(vd348, tptp_fun_Vd196_0(vd347, vd348)) = vd347),
% 0.41/0.62 inference(symmetry,[status(thm)],[35])).
% 0.41/0.62 tff(37,plain,
% 0.41/0.62 (vplus(vd345, vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))) = vplus(vd345, vd347)),
% 0.41/0.62 inference(monotonicity,[status(thm)],[36])).
% 0.41/0.62 tff(38,plain,
% 0.41/0.62 ((~![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))) | (vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vd347, vd348)) = vplus(vd345, vplus(vd348, tptp_fun_Vd196_0(vd347, vd348))))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(39,plain,
% 0.41/0.62 (vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vd347, vd348)) = vplus(vd345, vplus(vd348, tptp_fun_Vd196_0(vd347, vd348)))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[38, 7])).
% 0.41/0.62 tff(40,plain,
% 0.41/0.62 (vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vd347, vd348)) = vplus(vd347, vd345)),
% 0.41/0.62 inference(transitivity,[status(thm)],[39, 37, 12])).
% 0.41/0.62 tff(41,plain,
% 0.41/0.62 (vplus(vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vd347, vd348)), tptp_fun_Vd196_0(vd344, vd345)) = vplus(vplus(vd347, vd345), tptp_fun_Vd196_0(vd344, vd345))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[40])).
% 0.41/0.62 tff(42,plain,
% 0.41/0.62 (vplus(vplus(vd347, vd345), tptp_fun_Vd196_0(vd344, vd345)) = vplus(vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vd347, vd348)), tptp_fun_Vd196_0(vd344, vd345))),
% 0.41/0.62 inference(symmetry,[status(thm)],[41])).
% 0.41/0.62 tff(43,plain,
% 0.41/0.62 ((~![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))) | (vplus(vplus(vd347, vd345), tptp_fun_Vd196_0(vd344, vd345)) = vplus(vd347, vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(44,plain,
% 0.41/0.62 (vplus(vplus(vd347, vd345), tptp_fun_Vd196_0(vd344, vd345)) = vplus(vd347, vplus(vd345, tptp_fun_Vd196_0(vd344, vd345)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[43, 7])).
% 0.41/0.63 tff(45,plain,
% 0.41/0.63 (vplus(vd347, vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))) = vplus(vplus(vd347, vd345), tptp_fun_Vd196_0(vd344, vd345))),
% 0.41/0.63 inference(symmetry,[status(thm)],[44])).
% 0.41/0.63 tff(46,plain,
% 0.41/0.63 ((~![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))) | (~((~((~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))))) | (~(greater(vd344, vd345) | ![Vd196: $i] : (~(vd344 = vplus(vd345, Vd196)))))))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(47,plain,
% 0.41/0.63 (~((~((~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))))) | (~(greater(vd344, vd345) | ![Vd196: $i] : (~(vd344 = vplus(vd345, Vd196))))))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[46, 25])).
% 0.41/0.63 tff(48,plain,
% 0.41/0.63 (((~((~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))))) | (~(greater(vd344, vd345) | ![Vd196: $i] : (~(vd344 = vplus(vd345, Vd196)))))) | ((~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(49,plain,
% 0.41/0.63 ((~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.41/0.63 tff(50,plain,
% 0.41/0.63 (greater(vd344, vd345) <=> greater(vd344, vd345)),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(51,axiom,(greater(vd344, vd345)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conjunct1(211), 346, 0)'')).
% 0.41/0.63 tff(52,plain,
% 0.41/0.63 (greater(vd344, vd345)),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.41/0.63 tff(53,plain,
% 0.41/0.63 ((~((~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))))) | (~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345)))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(54,plain,
% 0.41/0.63 ((~((~greater(vd344, vd345)) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))))) | (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.41/0.63 tff(55,plain,
% 0.41/0.63 (vd344 = vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[54, 49])).
% 0.41/0.63 tff(56,plain,
% 0.41/0.63 (vplus(vd345, tptp_fun_Vd196_0(vd344, vd345)) = vd344),
% 0.41/0.63 inference(symmetry,[status(thm)],[55])).
% 0.41/0.63 tff(57,plain,
% 0.41/0.63 (vplus(vd347, vplus(vd345, tptp_fun_Vd196_0(vd344, vd345))) = vplus(vd347, vd344)),
% 0.41/0.63 inference(monotonicity,[status(thm)],[56])).
% 0.41/0.63 tff(58,plain,
% 0.41/0.63 (vplus(vd347, vd344) = vplus(vd347, vplus(vd345, tptp_fun_Vd196_0(vd344, vd345)))),
% 0.41/0.63 inference(symmetry,[status(thm)],[57])).
% 0.41/0.63 tff(59,plain,
% 0.41/0.63 (^[Vd78: $i, Vd79: $i] : refl((vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)))),
% 0.41/0.63 inference(bind,[status(th)],[])).
% 0.41/0.63 tff(60,plain,
% 0.41/0.63 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.41/0.63 inference(quant_intro,[status(thm)],[59])).
% 0.41/0.63 tff(61,plain,
% 0.41/0.63 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(62,axiom,(![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(61, 0), 0)'')).
% 0.41/0.63 tff(63,plain,
% 0.41/0.63 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.41/0.63 tff(64,plain,(
% 0.41/0.63 ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.41/0.63 inference(skolemize,[status(sab)],[63])).
% 0.41/0.63 tff(65,plain,
% 0.41/0.63 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.41/0.63 tff(66,plain,
% 0.41/0.63 ((~![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))) | (vplus(vd347, vd344) = vplus(vd344, vd347))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(67,plain,
% 0.41/0.63 (vplus(vd347, vd344) = vplus(vd344, vd347)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.41/0.63 tff(68,plain,
% 0.41/0.63 (vplus(vd344, vd347) = vplus(vd347, vd344)),
% 0.41/0.63 inference(symmetry,[status(thm)],[67])).
% 0.41/0.63 tff(69,plain,
% 0.41/0.63 (vplus(vd344, vd347) = vplus(vplus(vd345, vd348), vplus(tptp_fun_Vd196_0(vd347, vd348), tptp_fun_Vd196_0(vd344, vd345)))),
% 0.41/0.63 inference(transitivity,[status(thm)],[68, 58, 45, 42, 9])).
% 0.41/0.63 tff(70,plain,
% 0.41/0.63 ((~![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_0(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))) | (~((~((~greater(vplus(vd344, vd347), vplus(vd345, vd348))) | (vplus(vd344, vd347) = vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vplus(vd344, vd347), vplus(vd345, vd348)))))) | (~(greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196)))))))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(71,plain,
% 0.41/0.63 (~((~((~greater(vplus(vd344, vd347), vplus(vd345, vd348))) | (vplus(vd344, vd347) = vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vplus(vd344, vd347), vplus(vd345, vd348)))))) | (~(greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196))))))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[70, 25])).
% 0.41/0.63 tff(72,plain,
% 0.41/0.63 (((~((~greater(vplus(vd344, vd347), vplus(vd345, vd348))) | (vplus(vd344, vd347) = vplus(vplus(vd345, vd348), tptp_fun_Vd196_0(vplus(vd344, vd347), vplus(vd345, vd348)))))) | (~(greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196)))))) | (greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196))))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(73,plain,
% 0.41/0.63 (greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.41/0.63 tff(74,plain,
% 0.41/0.63 ((~greater(vplus(vd344, vd347), vplus(vd345, vd348))) <=> (~greater(vplus(vd344, vd347), vplus(vd345, vd348)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(75,axiom,(~greater(vplus(vd344, vd347), vplus(vd345, vd348))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(214, 352, 0)'')).
% 0.41/0.63 tff(76,plain,
% 0.41/0.63 (~greater(vplus(vd344, vd347), vplus(vd345, vd348))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.41/0.63 tff(77,plain,
% 0.41/0.63 ((~(greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196))))) | greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196)))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(78,plain,
% 0.41/0.63 ((~(greater(vplus(vd344, vd347), vplus(vd345, vd348)) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196))))) | ![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.41/0.63 tff(79,plain,
% 0.41/0.63 (![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[78, 73])).
% 0.41/0.63 tff(80,plain,
% 0.41/0.63 ((~![Vd196: $i] : (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), Vd196)))) | (~(vplus(vd344, vd347) = vplus(vplus(vd345, vd348), vplus(tptp_fun_Vd196_0(vd347, vd348), tptp_fun_Vd196_0(vd344, vd345)))))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(81,plain,
% 0.41/0.63 ($false),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[80, 79, 69])).
% 0.41/0.63 % SZS output end Proof
% 0.48/0.63 % E exiting
%------------------------------------------------------------------------------