%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM847+1 : TPTP v9.0.0. Released v4.1.0.
% 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 05:22:12 AM UTC 2025
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM847+1 : TPTP v9.0.0. Released v4.1.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 02:01:55 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(vplus_type, type, (
% 0.22/0.42 vplus: ( $i * $i ) > $i)).
% 0.22/0.42 tff(vd436_type, type, (
% 0.22/0.42 vd436: $i)).
% 0.22/0.42 tff(vmul_type, type, (
% 0.22/0.42 vmul: ( $i * $i ) > $i)).
% 0.22/0.42 tff(vd439_type, type, (
% 0.22/0.42 vd439: $i)).
% 0.22/0.42 tff(vd437_type, type, (
% 0.22/0.42 vd437: $i)).
% 0.22/0.42 tff(1,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(2,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.42 tff(3,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 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)'')).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.42 tff(6,plain,(
% 0.22/0.42 ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[5])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.42 tff(8,plain,
% 0.22/0.42 ((~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))) <=> (~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(9,axiom,(~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(286, 441, 3)'')).
% 0.22/0.42 tff(10,plain,
% 0.22/0.42 (~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.22/0.42 tff(11,plain,
% 0.22/0.42 ((~![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))) | (vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(12,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[11, 10, 7])).
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------