%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL390-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:14 AM UTC 2026
% Result : Unsatisfiable 6.34s 2.81s
% Output : Refutation 13.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 6
% Syntax : Number of formulae : 104 ( 104 unt; 0 def)
% Number of atoms : 104 ( 103 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 279 ( 279 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0,X1] : ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f3,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
fof(f5,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
fof(f7,plain,
! [X0] : true = is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
fof(f9,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_53) ).
fof(f11,plain,
true != is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),true),
inference(superposition,[],[f3,f5]) ).
fof(f16,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(superposition,[],[f3,f9]) ).
fof(f22,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,is_a_theorem(X2),true),
inference(forward_demodulation,[],[f16,f1]) ).
fof(f26,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),
inference(forward_demodulation,[],[f12,f1]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),true),
inference(superposition,[],[f26,f5]) ).
fof(f28,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X1),X2),X0),implies(X1,X0))),true),
inference(superposition,[],[f26,f9]) ).
fof(f29,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X0),implies(implies(not(X1),X1),X0))),true),
inference(superposition,[],[f26,f7]) ).
fof(f32,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,X0),implies(implies(not(X1),X1),X0))),
inference(forward_demodulation,[],[f29,f1]) ).
fof(f33,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(not(X1),X2),X0),implies(X1,X0))),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f34,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),
inference(forward_demodulation,[],[f27,f1]) ).
fof(f38,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(superposition,[],[f3,f32]) ).
fof(f39,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)),X2)),true,is_a_theorem(X2),true),
inference(forward_demodulation,[],[f38,f1]) ).
fof(f43,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,is_a_theorem(implies(implies(X2,X0),X3)),true),true),
inference(superposition,[],[f3,f34]) ).
fof(f47,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,is_a_theorem(implies(implies(X2,X0),X3)),true),
inference(forward_demodulation,[],[f43,f1]) ).
fof(f50,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X0),X1),X2)),true,is_a_theorem(implies(X0,X2)),true),true),
inference(superposition,[],[f3,f33]) ).
fof(f54,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(not(X0),X1),X2)),true,is_a_theorem(implies(X0,X2)),true),
inference(forward_demodulation,[],[f50,f1]) ).
fof(f56,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(X0,X1)),implies(implies(X2,X0),implies(X3,implies(X2,X1))))),true),
inference(superposition,[],[f47,f34]) ).
fof(f59,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,not(X0)),implies(X0,implies(X1,X2)))),true),
inference(superposition,[],[f47,f33]) ).
fof(f68,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,not(X0)),implies(X0,implies(X1,X2)))),
inference(forward_demodulation,[],[f59,f1]) ).
fof(f71,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(X0,X1)),implies(implies(X2,X0),implies(X3,implies(X2,X1))))),
inference(forward_demodulation,[],[f56,f1]) ).
fof(f81,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2)))),true),true),
inference(superposition,[],[f3,f71]) ).
fof(f88,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2)))),true),
inference(forward_demodulation,[],[f81,f1]) ).
fof(f91,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X0),X0)),implies(implies(X0,X1),implies(X2,X1)))),true),
inference(superposition,[],[f88,f32]) ).
fof(f109,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X0),X0)),implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f91,f1]) ).
fof(f114,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),true),
inference(superposition,[],[f3,f109]) ).
fof(f121,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),
inference(forward_demodulation,[],[f114,f1]) ).
fof(f153,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X0,implies(not(X1),X2)))),true),
inference(superposition,[],[f54,f68]) ).
fof(f155,plain,
! [X0] : true = ifeq(true,true,is_a_theorem(implies(X0,X0)),true),
inference(superposition,[],[f54,f7]) ).
fof(f166,plain,
! [X0] : true = is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[],[f155,f1]) ).
fof(f168,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(X0,implies(not(X1),X2)))),
inference(forward_demodulation,[],[f153,f1]) ).
fof(f179,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,ifeq(true,true,is_a_theorem(X1),true),true),
inference(superposition,[],[f3,f166]) ).
fof(f180,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(X1),true),
inference(forward_demodulation,[],[f179,f1]) ).
fof(f256,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),true),
inference(superposition,[],[f180,f168]) ).
fof(f269,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),
inference(forward_demodulation,[],[f256,f1]) ).
fof(f405,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X2,X2),X0),implies(X1,X0))),true),
inference(superposition,[],[f121,f269]) ).
fof(f423,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X2,X2),X0),implies(X1,X0))),
inference(forward_demodulation,[],[f405,f1]) ).
fof(f435,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),true),
inference(superposition,[],[f39,f423]) ).
fof(f449,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(forward_demodulation,[],[f435,f1]) ).
fof(f507,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X0,implies(X1,X2)))),true),
inference(superposition,[],[f88,f449]) ).
fof(f523,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X0,implies(X1,X2)))),
inference(forward_demodulation,[],[f507,f1]) ).
fof(f534,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X2),X0),implies(X1,implies(implies(X0,X2),X2)))),true),
inference(superposition,[],[f47,f523]) ).
fof(f544,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(not(X2),X0),implies(X1,implies(implies(X0,X2),X2)))),
inference(forward_demodulation,[],[f534,f1]) ).
fof(f558,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X2,implies(X0,implies(implies(X1,X2),X2)))),true),
inference(superposition,[],[f54,f544]) ).
fof(f571,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X2,implies(X0,implies(implies(X1,X2),X2)))),
inference(forward_demodulation,[],[f558,f1]) ).
fof(f577,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X2,X1),X1),X0),implies(X1,X0))),true),
inference(superposition,[],[f121,f571]) ).
fof(f611,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X2,X1),X1),X0),implies(X1,X0))),
inference(forward_demodulation,[],[f577,f1]) ).
fof(f625,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X1,implies(X2,X1)))),true),
inference(superposition,[],[f47,f611]) ).
fof(f637,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X1,implies(X2,X1)))),
inference(forward_demodulation,[],[f625,f1]) ).
fof(f656,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X1,X0))),true),
inference(superposition,[],[f22,f637]) ).
fof(f671,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_demodulation,[],[f656,f1]) ).
fof(f682,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X2,X1),X0),implies(X1,X0))),true),
inference(superposition,[],[f26,f671]) ).
fof(f694,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X2,X1),X0),implies(X1,X0))),
inference(forward_demodulation,[],[f682,f1]) ).
fof(f725,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(X1,X2)),true),true),
inference(superposition,[],[f3,f694]) ).
fof(f740,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(X1,X2)),true),
inference(forward_demodulation,[],[f725,f1]) ).
fof(f815,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X0,implies(implies(X1,X2),X2)))),true),
inference(superposition,[],[f740,f544]) ).
fof(f870,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(X0,implies(implies(X1,X2),X2)))),
inference(forward_demodulation,[],[f815,f1]) ).
fof(f1014,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X0),implies(X1,X0))),true),
inference(superposition,[],[f121,f870]) ).
fof(f1051,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X0),implies(X1,X0))),
inference(forward_demodulation,[],[f1014,f1]) ).
fof(f1118,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f47,f1051]) ).
fof(f1130,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f1118,f1]) ).
fof(f1148,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true),true),
inference(superposition,[],[f3,f1130]) ).
fof(f1149,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(not(X0),implies(X0,X1))),true),
inference(superposition,[],[f22,f1130]) ).
fof(f1168,plain,
! [X0,X1] : true = is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(forward_demodulation,[],[f1149,f1]) ).
fof(f1169,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true),
inference(forward_demodulation,[],[f1148,f1]) ).
fof(f1181,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X0),implies(not(X1),X0))),true),
inference(superposition,[],[f26,f1168]) ).
fof(f1193,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X2),X0),implies(not(X1),X0))),
inference(forward_demodulation,[],[f1181,f1]) ).
fof(f1230,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X0),implies(implies(implies(X1,X2),X1),X0))),true),
inference(superposition,[],[f121,f1193]) ).
fof(f1260,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,X0),implies(implies(implies(X1,X2),X1),X0))),
inference(forward_demodulation,[],[f1230,f1]) ).
fof(f1374,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X1),X0),X0)),true),
inference(superposition,[],[f180,f1260]) ).
fof(f1403,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X1),X0),X0)),
inference(forward_demodulation,[],[f1374,f1]) ).
fof(f1473,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),true),
inference(superposition,[],[f47,f1403]) ).
fof(f1493,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_demodulation,[],[f1473,f1]) ).
fof(f1506,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X0,X1))),true,is_a_theorem(implies(X0,X1)),true),true),
inference(superposition,[],[f3,f1493]) ).
fof(f1519,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X0,X1))),true,is_a_theorem(implies(X0,X1)),true),
inference(forward_demodulation,[],[f1506,f1]) ).
fof(f1529,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),true),
inference(superposition,[],[f1519,f544]) ).
fof(f1576,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(forward_demodulation,[],[f1529,f1]) ).
fof(f1810,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X0),implies(implies(not(X0),X1),X0))),true),
inference(superposition,[],[f1169,f1576]) ).
fof(f1834,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,X0),implies(implies(not(X0),X1),X0))),
inference(forward_demodulation,[],[f1810,f1]) ).
fof(f1839,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X1),X0)),implies(implies(X0,X1),implies(X2,X1)))),true),
inference(superposition,[],[f88,f1834]) ).
fof(f1870,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X1),X0)),implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f1839,f1]) ).
fof(f1875,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X2))),true,is_a_theorem(implies(implies(X2,X1),implies(X0,X1))),true),true),
inference(superposition,[],[f3,f1870]) ).
fof(f1898,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X2))),true,is_a_theorem(implies(implies(X2,X1),implies(X0,X1))),true),
inference(forward_demodulation,[],[f1875,f1]) ).
fof(f2233,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X0,X1),X2),X0))),true),
inference(superposition,[],[f1898,f1193]) ).
fof(f2316,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X0,X1),X2),X0))),
inference(forward_demodulation,[],[f2233,f1]) ).
fof(f2321,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X2),X1),implies(implies(X1,X0),X0))),true),
inference(superposition,[],[f1169,f2316]) ).
fof(f2355,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X2),X1),implies(implies(X1,X0),X0))),
inference(forward_demodulation,[],[f2321,f1]) ).
fof(f2617,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X0),implies(implies(implies(X1,X2),X0),X0))),true),
inference(superposition,[],[f47,f2355]) ).
fof(f2629,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,X0),implies(implies(implies(X1,X2),X0),X0))),
inference(forward_demodulation,[],[f2617,f1]) ).
fof(f2643,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(implies(X0,X3),X1)),implies(implies(X0,X1),implies(X2,X1)))),true),
inference(superposition,[],[f88,f2629]) ).
fof(f2674,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(implies(X0,X3),X1)),implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f2643,f1]) ).
fof(f2691,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X0),X1),implies(implies(X0,X1),X1))),true),
inference(superposition,[],[f39,f2674]) ).
fof(f2708,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(not(X0),X1),implies(implies(X0,X1),X1))),
inference(forward_demodulation,[],[f2691,f1]) ).
fof(f2714,plain,
$false,
inference(backward_subsumption_resolution,[],[f11,f2708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL390-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 % Computer : n007.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 15:37:10 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.34/2.80 % (1604726)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.34/2.80 % (1604735)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1706943571:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.34/2.80 % (1604732)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4031982436:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.34/2.80 % (1604736)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1053885720:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.34/2.80 % (1604731)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1401808262:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.34/2.80 % (1604733)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3483738943:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.34/2.80 % (1604734)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2227770277:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.34/2.80 % (1604737)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1022357477:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.34/2.80 % (1604735)Instruction limit reached!
% 6.34/2.80 % (1604735)------------------------------
% 6.34/2.80 % (1604735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/2.80 % (1604735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/2.80 % (1604735)CaDiCaL version: 2.1.3
% 6.34/2.80 % (1604735)Termination reason: Instruction limit
% 6.34/2.80 % (1604735)Termination phase: Saturation
% 6.34/2.80 % (1604735)Time elapsed: 0.094 s
% 6.34/2.80 % (1604735)Peak memory usage: 90 MB
% 6.34/2.80 % (1604735)Instructions burned: 181 (million)
% 6.34/2.80 % (1604734)Instruction limit reached!
% 6.34/2.80 % (1604734)------------------------------
% 6.34/2.80 % (1604734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/2.80 % (1604734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/2.80 % (1604734)CaDiCaL version: 2.1.3
% 6.34/2.80 % (1604734)Termination reason: Instruction limit
% 6.34/2.80 % (1604734)Termination phase: Saturation
% 6.34/2.80 % (1604734)Time elapsed: 0.135 s
% 6.34/2.80 % (1604734)Peak memory usage: 89 MB
% 6.34/2.80 % (1604734)Instructions burned: 136 (million)
% 6.34/2.80 % (1604736)Instruction limit reached!
% 6.34/2.80 % (1604736)------------------------------
% 6.34/2.80 % (1604736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/2.80 % (1604736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/2.80 % (1604736)CaDiCaL version: 2.1.3
% 6.34/2.80 % (1604736)Termination reason: Instruction limit
% 6.34/2.80 % (1604736)Termination phase: Saturation
% 6.34/2.80 % (1604736)Time elapsed: 0.250 s
% 6.34/2.80 % (1604736)Peak memory usage: 90 MB
% 6.34/2.80 % (1604736)Instructions burned: 258 (million)
% 6.34/2.80 % (1604747)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1651559539:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 6.34/2.80 % (1604748)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1534783128:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 6.34/2.80 % (1604749)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=573234444:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 6.34/2.80 % (1604749)Instruction limit reached!
% 6.34/2.80 % (1604749)------------------------------
% 6.34/2.80 % (1604749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/2.80 % (1604749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/2.80 % (1604749)CaDiCaL version: 2.1.3
% 6.34/2.80 % (1604749)Termination reason: Instruction limit
% 6.34/2.80 % (1604749)Termination phase: Saturation
% 6.34/2.80 % (1604749)Time elapsed: 0.189 s
% 6.34/2.80 % (1604749)Peak memory usage: 88 MB
% 6.34/2.80 % (1604749)Instructions burned: 216 (million)
% 6.34/2.80 % (1604753)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=2190618270:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 6.34/2.80 % (1604737)Instruction limit reached!
% 6.34/2.80 % (1604737)------------------------------
% 6.34/2.80 % (1604737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/2.80 % (1604737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/2.80 % (1604737)CaDiCaL version: 2.1.3
% 6.34/2.80 % (1604737)Termination reason: Instruction limit
% 6.34/2.80 % (1604737)Termination phase: Saturation
% 6.34/2.80 % (1604737)Time elapsed: 1.125 s
% 6.34/2.80 % (1604737)Peak memory usage: 98 MB
% 6.34/2.80 % (1604737)Instructions burned: 1187 (million)
% 6.34/2.80 % (1604747)First to succeed.
% 6.34/2.80 % (1604747)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1604726"
% 6.34/2.80 % (1604753)Instruction limit reached!
% 6.34/2.81 % (1604753)------------------------------
% 6.34/2.81 % (1604753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/2.81 % (1604753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/2.81 % (1604753)CaDiCaL version: 2.1.3
% 6.34/2.81 % (1604753)Termination reason: Instruction limit
% 6.34/2.81 % (1604753)Termination phase: Saturation
% 6.34/2.81 % (1604753)Time elapsed: 0.296 s
% 6.34/2.81 % (1604753)Peak memory usage: 94 MB
% 6.34/2.81 % (1604753)Instructions burned: 318 (million)
% 6.34/2.81 % (1604755)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3140260764:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/12125Mi)
% 6.34/2.81 % (1604747)Refutation found. Thanks to Tanya!
% 6.34/2.81 % SZS status Unsatisfiable for theBenchmark
% 6.34/2.81 % SZS output start Proof for theBenchmark
% See solution above
% 13.74/3.08 % (1604747)------------------------------
% 13.74/3.08 % (1604747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.74/3.08 % (1604747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.74/3.08 % (1604747)CaDiCaL version: 2.1.3
% 13.74/3.08 % (1604747)Termination reason: Refutation
% 13.74/3.08 % (1604747)Time elapsed: 1.011 s
% 13.74/3.08 % (1604747)Peak memory usage: 137 MB
% 13.74/3.08 % (1604747)Instructions burned: 1677 (million)
% 13.74/3.08 % (1604747)------------------------------
% 13.74/3.08 % (1604747)------------------------------
% 13.74/3.08 % (1604726)Success in time 1.825 s
% 13.74/3.08 % Vampire exiting
%------------------------------------------------------------------------------