%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL054-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 11:51:02 AM UTC 2026
% Result : Unsatisfiable 12.53s 2.63s
% Output : Refutation 12.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 6
% Syntax : Number of formulae : 117 ( 117 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 325 ( 325 !; 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(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_35) ).
fof(f11,plain,
true != is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))),
inference(reorient_equations,[],[f10]) ).
fof(f13,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(f15,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(f16,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true),
inference(superposition,[],[f3,f5]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),X3)),true,is_a_theorem(X3),true),
inference(forward_demodulation,[],[f16,f1]) ).
fof(f23,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,[],[f15,f1]) ).
fof(f25,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,[],[f13,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,[],[f22,f5]) ).
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(f35,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(f42,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,[],[f35,f1]) ).
fof(f44,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,[],[f42,f34]) ).
fof(f53,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,[],[f44,f1]) ).
fof(f55,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,f53]) ).
fof(f65,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,[],[f55,f1]) ).
fof(f66,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,not(X0)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f65,f9]) ).
fof(f82,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,not(X0)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f66,f1]) ).
fof(f83,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f25,f9]) ).
fof(f87,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),true),
inference(superposition,[],[f25,f7]) ).
fof(f94,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(forward_demodulation,[],[f87,f1]) ).
fof(f98,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f83,f1]) ).
fof(f101,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,[],[f65,f94]) ).
fof(f115,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,[],[f101,f1]) ).
fof(f121,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,f115]) ).
fof(f129,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,[],[f121,f1]) ).
fof(f195,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,f98]) ).
fof(f208,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,[],[f195,f1]) ).
fof(f341,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),true),
inference(superposition,[],[f208,f82]) ).
fof(f343,plain,
! [X0] : true = ifeq(true,true,is_a_theorem(implies(X0,X0)),true),
inference(superposition,[],[f208,f7]) ).
fof(f358,plain,
! [X0] : true = is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[],[f343,f1]) ).
fof(f360,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(forward_demodulation,[],[f341,f1]) ).
fof(f387,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,f358]) ).
fof(f388,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(X1),true),
inference(forward_demodulation,[],[f387,f1]) ).
fof(f439,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),true),
inference(superposition,[],[f388,f360]) ).
fof(f457,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),
inference(forward_demodulation,[],[f439,f1]) ).
fof(f484,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f129,f457]) ).
fof(f524,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f484,f1]) ).
fof(f529,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X0,X0),X1),X2))),true),
inference(superposition,[],[f129,f524]) ).
fof(f536,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(implies(X2,X1)),true),true),
inference(superposition,[],[f3,f524]) ).
fof(f555,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(implies(X2,X1)),true),
inference(forward_demodulation,[],[f536,f1]) ).
fof(f559,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X0,X0),X1),X2))),
inference(forward_demodulation,[],[f529,f1]) ).
fof(f633,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(implies(X2,X2),X0)),implies(implies(X0,X1),implies(X3,X1)))),true),
inference(superposition,[],[f65,f559]) ).
fof(f662,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(implies(X2,X2),X0)),implies(implies(X0,X1),implies(X3,X1)))),
inference(forward_demodulation,[],[f633,f1]) ).
fof(f740,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(implies(X1,X1),X2))),true,is_a_theorem(implies(implies(X2,X3),implies(X0,X3))),true),true),
inference(superposition,[],[f3,f662]) ).
fof(f759,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(implies(X1,X1),X2))),true,is_a_theorem(implies(implies(X2,X3),implies(X0,X3))),true),
inference(forward_demodulation,[],[f740,f1]) ).
fof(f964,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(not(X0),X0),X0))),true),
inference(superposition,[],[f555,f94]) ).
fof(f1030,plain,
! [X0,X1] : true = is_a_theorem(implies(X1,implies(implies(not(X0),X0),X0))),
inference(forward_demodulation,[],[f964,f1]) ).
fof(f1080,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X1),X1)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f65,f1030]) ).
fof(f1116,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X1),X1)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f1080,f1]) ).
fof(f1132,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X2,implies(X0,X1))),true),true),
inference(superposition,[],[f3,f1116]) ).
fof(f1136,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),X0),implies(X2,implies(implies(X0,X1),X1)))),true),
inference(superposition,[],[f42,f1116]) ).
fof(f1148,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(not(X1),X0),implies(X2,implies(implies(X0,X1),X1)))),
inference(forward_demodulation,[],[f1136,f1]) ).
fof(f1151,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X2,implies(X0,X1))),true),
inference(forward_demodulation,[],[f1132,f1]) ).
fof(f1485,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X2,implies(implies(X1,X0),X0)))),true),
inference(superposition,[],[f208,f1148]) ).
fof(f1497,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(X2,implies(implies(X1,X0),X0)))),
inference(forward_demodulation,[],[f1485,f1]) ).
fof(f1514,plain,
! [X2,X3,X0] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X2,X0),X0),X3),implies(X0,X3))),true),
inference(superposition,[],[f759,f1497]) ).
fof(f1546,plain,
! [X2,X3,X0] : true = is_a_theorem(implies(implies(implies(implies(X2,X0),X0),X3),implies(X0,X3))),
inference(forward_demodulation,[],[f1514,f1]) ).
fof(f1573,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,[],[f42,f1546]) ).
fof(f1584,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X1,implies(X2,X1)))),
inference(forward_demodulation,[],[f1573,f1]) ).
fof(f1613,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X0,X1))),true),
inference(superposition,[],[f23,f1584]) ).
fof(f1632,plain,
! [X0,X1] : true = is_a_theorem(implies(X1,implies(X0,X1))),
inference(forward_demodulation,[],[f1613,f1]) ).
fof(f1653,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X0),X2),implies(X0,X2))),true),
inference(superposition,[],[f25,f1632]) ).
fof(f1680,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X0),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f1653,f1]) ).
fof(f1832,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,f1680]) ).
fof(f1851,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,[],[f1832,f1]) ).
fof(f2046,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X0),X0)))),true),
inference(superposition,[],[f1851,f1148]) ).
fof(f2164,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X0),X0)))),
inference(forward_demodulation,[],[f2046,f1]) ).
fof(f2182,plain,
! [X2,X3,X0] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X0,X2),X2),X3),implies(X0,X3))),true),
inference(superposition,[],[f759,f2164]) ).
fof(f2217,plain,
! [X2,X3,X0] : true = is_a_theorem(implies(implies(implies(implies(X0,X2),X2),X3),implies(X0,X3))),
inference(forward_demodulation,[],[f2182,f1]) ).
fof(f2246,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,[],[f42,f2217]) ).
fof(f2257,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f2246,f1]) ).
fof(f2289,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,f2257]) ).
fof(f2290,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(not(X0),implies(X0,X1))),true),
inference(superposition,[],[f23,f2257]) ).
fof(f2311,plain,
! [X0,X1] : true = is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(forward_demodulation,[],[f2290,f1]) ).
fof(f2312,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,[],[f2289,f1]) ).
fof(f2583,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),true),
inference(superposition,[],[f25,f2311]) ).
fof(f2594,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(forward_demodulation,[],[f2583,f1]) ).
fof(f2652,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X2,implies(implies(implies(X0,X1),X0),X0))),true),
inference(superposition,[],[f1151,f2594]) ).
fof(f2695,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X2,implies(implies(implies(X0,X1),X0),X0))),
inference(forward_demodulation,[],[f2652,f1]) ).
fof(f2701,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(implies(X1,X2),X1)),implies(X0,implies(X3,X1)))),true),
inference(superposition,[],[f65,f2695]) ).
fof(f2718,plain,
! [X3,X4] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X3,X4),X3),X3)),true),
inference(superposition,[],[f22,f2695]) ).
fof(f2732,plain,
! [X3,X4] : true = is_a_theorem(implies(implies(implies(X3,X4),X3),X3)),
inference(forward_demodulation,[],[f2718,f1]) ).
fof(f2740,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(implies(X1,X2),X1)),implies(X0,implies(X3,X1)))),
inference(forward_demodulation,[],[f2701,f1]) ).
fof(f2751,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),true),
inference(superposition,[],[f42,f2732]) ).
fof(f2781,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_demodulation,[],[f2751,f1]) ).
fof(f2801,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,f2781]) ).
fof(f2822,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X0,X1))),true,is_a_theorem(implies(X0,X1)),true),
inference(forward_demodulation,[],[f2801,f1]) ).
fof(f2860,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),true),
inference(superposition,[],[f2822,f1116]) ).
fof(f2921,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(forward_demodulation,[],[f2860,f1]) ).
fof(f3005,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X0,X1)),true),true),
inference(superposition,[],[f3,f2921]) ).
fof(f3033,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X0,X1)),true),
inference(forward_demodulation,[],[f3005,f1]) ).
fof(f3859,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,implies(implies(X1,X2),X1)),implies(X0,X1))),true),
inference(superposition,[],[f3033,f2740]) ).
fof(f3899,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,implies(implies(X1,X2),X1)),implies(X0,X1))),
inference(forward_demodulation,[],[f3859,f1]) ).
fof(f3934,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X0),implies(implies(X0,X1),X1))),true),
inference(superposition,[],[f42,f3899]) ).
fof(f3946,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X2),X0),implies(implies(X0,X1),X1))),
inference(forward_demodulation,[],[f3934,f1]) ).
fof(f3989,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X2,X1),X0),X0))),true),
inference(superposition,[],[f42,f3946]) ).
fof(f4001,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X2,X1),X0),X0))),
inference(forward_demodulation,[],[f3989,f1]) ).
fof(f4026,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(implies(X0,X2),X1)),implies(implies(X0,X1),implies(X3,X1)))),true),
inference(superposition,[],[f65,f4001]) ).
fof(f4064,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(implies(X0,X2),X1)),implies(implies(X0,X1),implies(X3,X1)))),
inference(forward_demodulation,[],[f4026,f1]) ).
fof(f4149,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X0,X2)),implies(implies(X0,X1),implies(X0,X2)))),true),
inference(superposition,[],[f22,f4064]) ).
fof(f4163,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,implies(X0,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(forward_demodulation,[],[f4149,f1]) ).
fof(f4204,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,X0),implies(implies(X2,implies(X0,X1)),implies(X2,X1)))),true),
inference(superposition,[],[f42,f4163]) ).
fof(f4216,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,X0),implies(implies(X2,implies(X0,X1)),implies(X2,X1)))),
inference(forward_demodulation,[],[f4204,f1]) ).
fof(f5210,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),true),
inference(superposition,[],[f2312,f4216]) ).
fof(f5253,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(forward_demodulation,[],[f5210,f1]) ).
fof(f5260,plain,
true != true,
inference(superposition,[],[f11,f5253]) ).
fof(f5303,plain,
$false,
inference(trivial_inequality_removal,[],[f5260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL054-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n015.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 15:23:15 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 12.53/2.63 % (1773663)Detected a unit-equality problem, will run specialized UEQ schedule.
% 12.53/2.63 % (1773689)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=1952646809:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 12.53/2.63 % (1773695)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=762872418:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 12.53/2.63 % (1773692)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2298319884:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 12.53/2.63 % (1773691)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3237682105:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 12.53/2.63 % (1773693)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1409289618:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 12.53/2.63 % (1773694)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2374170963:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 12.53/2.63 % (1773690)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=748820050:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 12.53/2.63 % (1773692)Instruction limit reached!
% 12.53/2.63 % (1773692)------------------------------
% 12.53/2.63 % (1773692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/2.63 % (1773692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.63 % (1773692)CaDiCaL version: 2.1.3
% 12.53/2.63 % (1773692)Termination reason: Instruction limit
% 12.53/2.63 % (1773692)Termination phase: Saturation
% 12.53/2.63 % (1773692)Time elapsed: 0.116 s
% 12.53/2.63 % (1773692)Peak memory usage: 89 MB
% 12.53/2.63 % (1773692)Instructions burned: 136 (million)
% 12.53/2.63 % (1773693)Instruction limit reached!
% 12.53/2.63 % (1773693)------------------------------
% 12.53/2.63 % (1773693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/2.63 % (1773693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.63 % (1773693)CaDiCaL version: 2.1.3
% 12.53/2.63 % (1773693)Termination reason: Instruction limit
% 12.53/2.63 % (1773693)Termination phase: Saturation
% 12.53/2.63 % (1773693)Time elapsed: 0.162 s
% 12.53/2.63 % (1773693)Peak memory usage: 90 MB
% 12.53/2.63 % (1773693)Instructions burned: 181 (million)
% 12.53/2.63 % (1773694)Instruction limit reached!
% 12.53/2.63 % (1773694)------------------------------
% 12.53/2.63 % (1773694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/2.63 % (1773694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.63 % (1773694)CaDiCaL version: 2.1.3
% 12.53/2.63 % (1773694)Termination reason: Instruction limit
% 12.53/2.63 % (1773694)Termination phase: Saturation
% 12.53/2.63 % (1773694)Time elapsed: 0.232 s
% 12.53/2.63 % (1773694)Peak memory usage: 91 MB
% 12.53/2.63 % (1773694)Instructions burned: 257 (million)
% 12.53/2.63 % (1773708)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2255378490:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 12.53/2.63 % (1773711)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=78275675:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 12.53/2.63 % (1773713)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=401533285:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 12.53/2.63 % (1773713)Instruction limit reached!
% 12.53/2.63 % (1773713)------------------------------
% 12.53/2.63 % (1773713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/2.63 % (1773713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.63 % (1773713)CaDiCaL version: 2.1.3
% 12.53/2.63 % (1773713)Termination reason: Instruction limit
% 12.53/2.63 % (1773713)Termination phase: Saturation
% 12.53/2.63 % (1773713)Time elapsed: 0.113 s
% 12.53/2.63 % (1773713)Peak memory usage: 88 MB
% 12.53/2.63 % (1773713)Instructions burned: 217 (million)
% 12.53/2.63 % (1773720)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=1685214777:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2992 on theBenchmark for (2992ds/317Mi)
% 12.53/2.63 % (1773695)Instruction limit reached!
% 12.53/2.63 % (1773695)------------------------------
% 12.53/2.63 % (1773695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/2.63 % (1773695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.63 % (1773695)CaDiCaL version: 2.1.3
% 12.53/2.63 % (1773695)Termination reason: Instruction limit
% 12.53/2.63 % (1773695)Termination phase: Saturation
% 12.53/2.63 % (1773695)Time elapsed: 0.818 s
% 12.53/2.63 % (1773695)Peak memory usage: 98 MB
% 12.53/2.63 % (1773695)Instructions burned: 1189 (million)
% 12.53/2.63 % (1773723)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=2192376251:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 12.53/2.63 % (1773720)Instruction limit reached!
% 12.53/2.63 % (1773720)------------------------------
% 12.53/2.63 % (1773720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/2.63 % (1773720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.63 % (1773720)CaDiCaL version: 2.1.3
% 12.53/2.63 % (1773720)Termination reason: Instruction limit
% 12.53/2.63 % (1773720)Termination phase: Saturation
% 12.53/2.63 % (1773720)Time elapsed: 0.187 s
% 12.53/2.63 % (1773720)Peak memory usage: 94 MB
% 12.53/2.63 % (1773720)Instructions burned: 318 (million)
% 12.53/2.63 % (1773730)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=812075106:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2989 on theBenchmark for (2989ds/2836Mi)
% 12.53/2.63 % (1773690)First to succeed.
% 12.53/2.63 % (1773690)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1773663"
% 12.53/2.63 % (1773708)Also succeeded, but the first one will report.
% 12.53/2.63 % (1773690)Refutation found. Thanks to Tanya!
% 12.53/2.63 % SZS status Unsatisfiable for theBenchmark
% 12.53/2.63 % SZS output start Proof for theBenchmark
% See solution above
% 12.83/2.72 % (1773690)------------------------------
% 12.83/2.72 % (1773690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.83/2.72 % (1773690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.83/2.72 % (1773690)CaDiCaL version: 2.1.3
% 12.83/2.72 % (1773690)Termination reason: Refutation
% 12.83/2.72 % (1773690)Time elapsed: 1.261 s
% 12.83/2.72 % (1773690)Peak memory usage: 137 MB
% 12.83/2.72 % (1773690)Instructions burned: 1775 (million)
% 12.83/2.72 % (1773690)------------------------------
% 12.83/2.72 % (1773690)------------------------------
% 12.83/2.72 % (1773663)Success in time 1.733 s
% 12.83/2.72 % Vampire exiting
%------------------------------------------------------------------------------