%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL375-10 : 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 : n009.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 11:52:09 AM UTC 2026
% Result : Unsatisfiable 28.55s 5.79s
% Output : Refutation 33.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 6
% Syntax : Number of formulae : 111 ( 111 unt; 0 def)
% Number of atoms : 111 ( 110 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 : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 321 ( 321 !; 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(implies(x,y),z),implies(implies(x,u),implies(implies(u,z),z)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_32) ).
fof(f11,plain,
true != is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,z),z)))),
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(f14,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(f15,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,[],[f14,f1]) ).
fof(f16,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(f17,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,[],[f16,f5]) ).
fof(f21,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,[],[f17,f1]) ).
fof(f24,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,f21]) ).
fof(f28,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,[],[f24,f1]) ).
fof(f31,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,[],[f28,f21]) ).
fof(f38,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,[],[f31,f1]) ).
fof(f42,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f16,f9]) ).
fof(f48,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f42,f1]) ).
fof(f51,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),true),
inference(superposition,[],[f16,f7]) ).
fof(f54,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)),true,ifeq(true,true,is_a_theorem(X1),true),true),
inference(superposition,[],[f3,f7]) ).
fof(f55,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)),true,is_a_theorem(X1),true),
inference(forward_demodulation,[],[f54,f1]) ).
fof(f57,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(forward_demodulation,[],[f51,f1]) ).
fof(f61,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,f38]) ).
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,[],[f61,f1]) ).
fof(f89,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,f57]) ).
fof(f97,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,[],[f89,f1]) ).
fof(f103,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),X0),implies(implies(X1,X2),implies(implies(X0,X1),X2)))),true),
inference(superposition,[],[f28,f97]) ).
fof(f106,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,f97]) ).
fof(f110,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,[],[f106,f1]) ).
fof(f113,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(not(X1),X0),implies(implies(X1,X2),implies(implies(X0,X1),X2)))),
inference(forward_demodulation,[],[f103,f1]) ).
fof(f223,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,f48]) ).
fof(f227,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,[],[f223,f1]) ).
fof(f234,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(implies(X0,X2),implies(implies(X1,X0),X2)))),true),
inference(superposition,[],[f227,f113]) ).
fof(f241,plain,
! [X0] : true = ifeq(true,true,is_a_theorem(implies(X0,X0)),true),
inference(superposition,[],[f227,f7]) ).
fof(f255,plain,
! [X0] : true = is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[],[f241,f1]) ).
fof(f262,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(implies(X0,X2),implies(implies(X1,X0),X2)))),
inference(forward_demodulation,[],[f234,f1]) ).
fof(f278,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,f255]) ).
fof(f279,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(X1),true),
inference(forward_demodulation,[],[f278,f1]) ).
fof(f318,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X0),X1),implies(implies(X2,implies(X0,X0)),X1))),true),
inference(superposition,[],[f279,f262]) ).
fof(f335,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X0),X1),implies(implies(X2,implies(X0,X0)),X1))),
inference(forward_demodulation,[],[f318,f1]) ).
fof(f349,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X0,X0)),implies(X0,X0))),true),
inference(superposition,[],[f279,f335]) ).
fof(f367,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,implies(X0,X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f349,f1]) ).
fof(f372,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X1,X1))),true),
inference(superposition,[],[f227,f367]) ).
fof(f389,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(X1,X1))),
inference(forward_demodulation,[],[f372,f1]) ).
fof(f452,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,X1),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f65,f389]) ).
fof(f456,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f16,f389]) ).
fof(f463,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f456,f1]) ).
fof(f465,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,X1),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f452,f1]) ).
fof(f476,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,[],[f110,f463]) ).
fof(f482,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,f463]) ).
fof(f488,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,[],[f482,f1]) ).
fof(f492,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X0,X0),X1),X2))),
inference(forward_demodulation,[],[f476,f1]) ).
fof(f793,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X2,implies(implies(implies(X1,X1),X0),X0))),true),
inference(superposition,[],[f488,f492]) ).
fof(f851,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X2,implies(implies(implies(X1,X1),X0),X0))),
inference(forward_demodulation,[],[f793,f1]) ).
fof(f879,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X2,implies(X0,X1)),X3),implies(implies(X0,X1),X3))),true),
inference(superposition,[],[f16,f465]) ).
fof(f887,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(X2,implies(X0,X1)),X3),implies(implies(X0,X1),X3))),
inference(forward_demodulation,[],[f879,f1]) ).
fof(f911,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X0,implies(X1,X2)),X3)),true,is_a_theorem(implies(implies(X1,X2),X3)),true),true),
inference(superposition,[],[f3,f887]) ).
fof(f917,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,implies(X1,X2)),X3)),true,is_a_theorem(implies(implies(X1,X2),X3)),true),
inference(forward_demodulation,[],[f911,f1]) ).
fof(f2513,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(implies(X1,X1),X2)),implies(X0,implies(X3,X2)))),true),
inference(superposition,[],[f65,f851]) ).
fof(f2540,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(implies(X1,X1),X2)),implies(X0,implies(X3,X2)))),
inference(forward_demodulation,[],[f2513,f1]) ).
fof(f2755,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),X1),implies(implies(X1,X2),implies(X0,X2)))),true),
inference(superposition,[],[f917,f97]) ).
fof(f2869,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(not(X1),X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_demodulation,[],[f2755,f1]) ).
fof(f2884,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1)))),true),
inference(superposition,[],[f227,f2869]) ).
fof(f2924,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f2884,f1]) ).
fof(f3079,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(X0,X3))),true),
inference(superposition,[],[f16,f2924]) ).
fof(f3100,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(X0,X3))),
inference(forward_demodulation,[],[f3079,f1]) ).
fof(f3148,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(X0,X3)),true),true),
inference(superposition,[],[f3,f3100]) ).
fof(f3171,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,is_a_theorem(implies(X0,X3)),true),
inference(forward_demodulation,[],[f3148,f1]) ).
fof(f3193,plain,
! [X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X3,implies(implies(X0,X1),X1)))),true),
inference(superposition,[],[f3171,f2540]) ).
fof(f3312,plain,
! [X3,X0,X1] : true = is_a_theorem(implies(X0,implies(X3,implies(implies(X0,X1),X1)))),
inference(forward_demodulation,[],[f3193,f1]) ).
fof(f4445,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f110,f3312]) ).
fof(f4479,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f4445,f1]) ).
fof(f4519,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,[],[f28,f4479]) ).
fof(f4565,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f4519,f1]) ).
fof(f4690,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(implies(X0,X1),implies(X0,X2)))),true),
inference(superposition,[],[f15,f4565]) ).
fof(f4701,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,f4565]) ).
fof(f4727,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,[],[f4701,f1]) ).
fof(f4734,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,X2),implies(implies(X0,X1),implies(X0,X2)))),
inference(forward_demodulation,[],[f4690,f1]) ).
fof(f4756,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(not(X0),X0)),implies(X1,X0))),true),
inference(superposition,[],[f55,f4734]) ).
fof(f4784,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X2,X0),implies(X2,X1))),true),true),
inference(superposition,[],[f3,f4734]) ).
fof(f4810,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X2,X0),implies(X2,X1))),true),
inference(forward_demodulation,[],[f4784,f1]) ).
fof(f4826,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,implies(not(X0),X0)),implies(X1,X0))),
inference(forward_demodulation,[],[f4756,f1]) ).
fof(f4866,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,f4826]) ).
fof(f4892,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,[],[f4866,f1]) ).
fof(f6424,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(not(X0),implies(X0,X1))),true),
inference(superposition,[],[f4727,f9]) ).
fof(f6525,plain,
! [X0,X1] : true = is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(forward_demodulation,[],[f6424,f1]) ).
fof(f6597,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),true),
inference(superposition,[],[f16,f6525]) ).
fof(f6624,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(forward_demodulation,[],[f6597,f1]) ).
fof(f6664,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X1),X0),X0)),true),
inference(superposition,[],[f4892,f6624]) ).
fof(f6704,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X1),X0),X0)),
inference(forward_demodulation,[],[f6664,f1]) ).
fof(f6755,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(implies(X0,X1),X0)),implies(X2,X0))),true),
inference(superposition,[],[f4810,f6704]) ).
fof(f6778,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(implies(X0,X1),X0)),implies(X2,X0))),
inference(forward_demodulation,[],[f6755,f1]) ).
fof(f7305,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,[],[f28,f6778]) ).
fof(f7359,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X2),X0),implies(implies(X0,X1),X1))),
inference(forward_demodulation,[],[f7305,f1]) ).
fof(f7412,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X2,X0),X0),X3),implies(implies(implies(X0,X1),X2),X3))),true),
inference(superposition,[],[f16,f7359]) ).
fof(f7424,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(implies(X0,X1),X2)),implies(X3,implies(implies(X2,X0),X0)))),true),
inference(superposition,[],[f4810,f7359]) ).
fof(f7434,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(implies(X0,X1),X2)),implies(X3,implies(implies(X2,X0),X0)))),
inference(forward_demodulation,[],[f7424,f1]) ).
fof(f7439,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X2,X0),X0),X3),implies(implies(implies(X0,X1),X2),X3))),
inference(forward_demodulation,[],[f7412,f1]) ).
fof(f8831,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X2,X3),X0),implies(implies(X0,X1),implies(implies(X1,X2),X2)))),true),
inference(superposition,[],[f28,f7434]) ).
fof(f8885,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(X2,X3),X0),implies(implies(X0,X1),implies(implies(X1,X2),X2)))),
inference(forward_demodulation,[],[f8831,f1]) ).
fof(f10234,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X0,X1),X1),X2)),true,is_a_theorem(implies(implies(implies(X1,X3),X0),X2)),true),true),
inference(superposition,[],[f3,f7439]) ).
fof(f10263,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),X1),X2)),true,is_a_theorem(implies(implies(implies(X1,X3),X0),X2)),true),
inference(forward_demodulation,[],[f10234,f1]) ).
fof(f10335,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X3),X0),implies(implies(X1,X2),implies(implies(X2,X0),X0)))),true),
inference(superposition,[],[f10263,f8885]) ).
fof(f10536,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X3),X0),implies(implies(X1,X2),implies(implies(X2,X0),X0)))),
inference(forward_demodulation,[],[f10335,f1]) ).
fof(f17547,plain,
true != true,
inference(superposition,[],[f11,f10536]) ).
fof(f17620,plain,
$false,
inference(trivial_inequality_removal,[],[f17547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL375-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:37:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 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
% 28.55/5.79 % (2189416)Detected a unit-equality problem, will run specialized UEQ schedule.
% 28.55/5.79 % (2189426)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3158163029:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 28.55/5.79 % (2189422)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=4120739081:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 28.55/5.79 % (2189421)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=2586009167:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 28.55/5.79 % (2189423)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3953682754:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 28.55/5.79 % (2189424)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2106139321:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 28.55/5.79 % (2189425)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=677151377:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 28.55/5.79 % (2189427)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=813606882:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 28.55/5.79 % (2189426)Instruction limit reached!
% 28.55/5.79 % (2189426)------------------------------
% 28.55/5.79 % (2189426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.55/5.79 % (2189426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.55/5.79 % (2189426)CaDiCaL version: 2.1.3
% 28.55/5.79 % (2189426)Termination reason: Instruction limit
% 28.55/5.79 % (2189426)Termination phase: Saturation
% 28.55/5.79 % (2189426)Time elapsed: 0.140 s
% 28.55/5.79 % (2189426)Peak memory usage: 91 MB
% 28.55/5.79 % (2189426)Instructions burned: 258 (million)
% 28.55/5.79 % (2189424)Instruction limit reached!
% 28.55/5.79 % (2189424)------------------------------
% 28.55/5.79 % (2189424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.55/5.79 % (2189424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.55/5.79 % (2189424)CaDiCaL version: 2.1.3
% 28.55/5.79 % (2189424)Termination reason: Instruction limit
% 28.55/5.79 % (2189424)Termination phase: Saturation
% 28.55/5.79 % (2189424)Time elapsed: 0.135 s
% 28.55/5.79 % (2189424)Peak memory usage: 89 MB
% 28.55/5.79 % (2189424)Instructions burned: 136 (million)
% 28.55/5.79 % (2189425)Instruction limit reached!
% 28.55/5.79 % (2189425)------------------------------
% 28.55/5.79 % (2189425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.55/5.79 % (2189425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.55/5.79 % (2189425)CaDiCaL version: 2.1.3
% 28.55/5.79 % (2189425)Termination reason: Instruction limit
% 28.55/5.79 % (2189425)Termination phase: Saturation
% 28.55/5.79 % (2189425)Time elapsed: 0.171 s
% 28.55/5.79 % (2189425)Peak memory usage: 90 MB
% 28.55/5.79 % (2189425)Instructions burned: 181 (million)
% 28.55/5.79 % (2189435)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3797341397:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 28.55/5.79 % (2189436)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=141689766:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 28.55/5.79 % (2189437)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1961447423:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 28.55/5.79 % (2189437)Instruction limit reached!
% 28.55/5.79 % (2189437)------------------------------
% 28.55/5.79 % (2189437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.55/5.79 % (2189437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.55/5.79 % (2189437)CaDiCaL version: 2.1.3
% 28.55/5.79 % (2189437)Termination reason: Instruction limit
% 28.55/5.79 % (2189437)Termination phase: Saturation
% 28.55/5.79 % (2189437)Time elapsed: 0.183 s
% 28.55/5.79 % (2189437)Peak memory usage: 88 MB
% 28.55/5.79 % (2189437)Instructions burned: 215 (million)
% 28.55/5.79 % (2189441)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=917784111: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)
% 28.55/5.79 % (2189427)Instruction limit reached!
% 28.55/5.79 % (2189427)------------------------------
% 28.55/5.79 % (2189427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.55/5.79 % (2189427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.55/5.79 % (2189427)CaDiCaL version: 2.1.3
% 28.55/5.79 % (2189427)Termination reason: Instruction limit
% 28.55/5.79 % (2189427)Termination phase: Saturation
% 28.55/5.79 % (2189427)Time elapsed: 1.102 s
% 28.55/5.79 % (2189427)Peak memory usage: 98 MB
% 28.55/5.79 % (2189427)Instructions burned: 1187 (million)
% 28.55/5.79 % (2189441)Instruction limit reached!
% 28.55/5.79 % (2189441)------------------------------
% 28.55/5.79 % (2189441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.55/5.79 % (2189441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.55/5.79 % (2189441)CaDiCaL version: 2.1.3
% 28.55/5.79 % (2189441)Termination reason: Instruction limit
% 28.55/5.79 % (2189441)Termination phase: Saturation
% 28.55/5.79 % (2189441)Time elapsed: 0.301 s
% 28.55/5.79 % (2189441)Peak memory usage: 94 MB
% 28.55/5.79 % (2189441)Instructions burned: 317 (million)
% 28.55/5.79 % (2189443)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=3757507697:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/12125Mi)
% 28.55/5.79 % (2189444)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2114860689:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2984 on theBenchmark for (2984ds/2836Mi)
% 28.55/5.79 % (2189435)Instruction limit reached!
% 28.55/5.79 % (2189435)------------------------------
% 28.55/5.79 % (2189435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.55/5.79 % (2189435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.55/5.79 % (2189435)CaDiCaL version: 2.1.3
% 28.55/5.79 % (2189435)Termination reason: Instruction limit
% 28.55/5.79 % (2189435)Termination phase: Saturation
% 28.55/5.79 % (2189435)Time elapsed: 1.777 s
% 28.55/5.79 % (2189435)Peak memory usage: 141 MB
% 28.55/5.79 % (2189435)Instructions burned: 2051 (million)
% 28.55/5.79 % (2189447)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=287579009:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2976 on theBenchmark for (2976ds/14534Mi)
% 28.55/5.79 % (2189436)First to succeed.
% 28.55/5.79 % (2189436)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2189416"
% 28.55/5.79 % (2189436)Refutation found. Thanks to Tanya!
% 28.55/5.79 % SZS status Unsatisfiable for theBenchmark
% 28.55/5.79 % SZS output start Proof for theBenchmark
% See solution above
% 33.46/6.15 % (2189436)------------------------------
% 33.46/6.15 % (2189436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.46/6.15 % (2189436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.46/6.15 % (2189436)CaDiCaL version: 2.1.3
% 33.46/6.15 % (2189436)Termination reason: Refutation
% 33.46/6.15 % (2189436)Time elapsed: 3.433 s
% 33.46/6.15 % (2189436)Peak memory usage: 153 MB
% 33.46/6.15 % (2189436)Instructions burned: 3426 (million)
% 33.46/6.15 % (2189436)------------------------------
% 33.46/6.15 % (2189436)------------------------------
% 33.46/6.15 % (2189416)Success in time 4.596 s
% 33.46/6.15 % Vampire exiting
%------------------------------------------------------------------------------