%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM846+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 05:22:12 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM846+2 : TPTP v9.0.0. Released v4.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 02:03:16 EDT 2025
% 0.19/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(vplus_type, type, (
% 0.19/0.37 vplus: ( $i * $i ) > $i)).
% 0.19/0.37 tff(vd436_type, type, (
% 0.19/0.37 vd436: $i)).
% 0.19/0.37 tff(vmul_type, type, (
% 0.19/0.37 vmul: ( $i * $i ) > $i)).
% 0.19/0.37 tff(vd439_type, type, (
% 0.19/0.37 vd439: $i)).
% 0.19/0.37 tff(vd437_type, type, (
% 0.19/0.37 vd437: $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 ((vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))) <=> (vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(2,axiom,(vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(285, 440, 0)'')).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (vplus(vmul(vd436, vd437), vmul(vd436, vd439)) = vmul(vd436, vplus(vd437, vd439))),
% 0.19/0.37 inference(symmetry,[status(thm)],[3])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[4])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)),
% 0.19/0.37 inference(symmetry,[status(thm)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 ((~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436))) <=> (~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(8,axiom,(~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(286, 441, 2)'')).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[9, 6])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------