%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM022+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /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 : Thu Sep 24 12:11:30 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 688 ( 98 equ)
% Maximal formula atoms : 158 ( 22 avg)
% Number of connectives : 853 ( 196 ~; 331 |; 315 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 17 con; 0-0 aty)
% Number of variables : 78 ( 0 sgn 6 !; 69 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ( ( sdtmndtplgtdt0(xa,xR,xc)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xc,xa,xR) )
& ( sdtmndtplgtdt0(xa,xR,xb)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,xb)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xb,xa,xR) ) )
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sdtmndtasgtdt0(xc,xR,X4)
& ( ( sdtmndtplgtdt0(xc,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xc,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xc,xR) ) )
| xc = X4 )
& sdtmndtasgtdt0(xb,xR,X4)
& ( ( sdtmndtplgtdt0(xb,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xb,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xb,xR) ) )
| xb = X4 )
& aNormalFormOfIn0(X4,X3,xR)
& ~ ? [X5] : aReductOfIn0(X5,X4,xR)
& sdtmndtasgtdt0(X3,xR,X4)
& ( ( sdtmndtplgtdt0(X3,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,X3,xR)
& aElement0(X5) )
| aReductOfIn0(X4,X3,xR) ) )
| X3 = X4 )
& aElement0(X4) )
& sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) )
& sdtmndtasgtdt0(X2,xR,xc)
& ( ( sdtmndtplgtdt0(X2,xR,xc)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,xc)
& aReductOfIn0(X3,X2,xR)
& aElement0(X3) )
| aReductOfIn0(xc,X2,xR) ) )
| X2 = xc )
& aReductOfIn0(X2,xa,xR)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xb)
& ( ( sdtmndtplgtdt0(X1,xR,xb)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,xb)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
| aReductOfIn0(xb,X1,xR) ) )
| X1 = xb )
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& ( ( sdtmndtplgtdt0(xa,xR,xc)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xc,xa,xR) ) )
| xa = xc )
& sdtmndtasgtdt0(xa,xR,xb)
& ( ( sdtmndtplgtdt0(xa,xR,xb)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xb)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xb,xa,xR) ) )
| xa = xb ) )
=> ? [X1] :
( ( sdtmndtasgtdt0(xc,xR,X1)
| sdtmndtplgtdt0(xc,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xc,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xc,xR)
| xc = X1 )
& ( sdtmndtasgtdt0(xb,xR,X1)
| sdtmndtplgtdt0(xb,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xb,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xb,xR)
| xb = X1 )
& aElement0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__731,hypothesis,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(c_0_2,negated_conjecture,
~ ( ( ( ( sdtmndtplgtdt0(xa,xR,xc)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xc,xa,xR) )
& ( sdtmndtplgtdt0(xa,xR,xb)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,xb)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xb,xa,xR) ) )
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sdtmndtasgtdt0(xc,xR,X4)
& ( ( sdtmndtplgtdt0(xc,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xc,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xc,xR) ) )
| xc = X4 )
& sdtmndtasgtdt0(xb,xR,X4)
& ( ( sdtmndtplgtdt0(xb,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xb,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xb,xR) ) )
| xb = X4 )
& aNormalFormOfIn0(X4,X3,xR)
& ~ ? [X5] : aReductOfIn0(X5,X4,xR)
& sdtmndtasgtdt0(X3,xR,X4)
& ( ( sdtmndtplgtdt0(X3,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,X3,xR)
& aElement0(X5) )
| aReductOfIn0(X4,X3,xR) ) )
| X3 = X4 )
& aElement0(X4) )
& sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) )
& sdtmndtasgtdt0(X2,xR,xc)
& ( ( sdtmndtplgtdt0(X2,xR,xc)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,xc)
& aReductOfIn0(X3,X2,xR)
& aElement0(X3) )
| aReductOfIn0(xc,X2,xR) ) )
| X2 = xc )
& aReductOfIn0(X2,xa,xR)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xb)
& ( ( sdtmndtplgtdt0(X1,xR,xb)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,xb)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
| aReductOfIn0(xb,X1,xR) ) )
| X1 = xb )
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& ( ( sdtmndtplgtdt0(xa,xR,xc)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xc,xa,xR) ) )
| xa = xc )
& sdtmndtasgtdt0(xa,xR,xb)
& ( ( sdtmndtplgtdt0(xa,xR,xb)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xb)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xb,xa,xR) ) )
| xa = xb ) )
=> ? [X1] :
( ( sdtmndtasgtdt0(xc,xR,X1)
| sdtmndtplgtdt0(xc,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xc,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xc,xR)
| xc = X1 )
& ( sdtmndtasgtdt0(xb,xR,X1)
| sdtmndtplgtdt0(xb,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xb,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xb,xR)
| xb = X1 )
& aElement0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_3,plain,
( epred1_0
<=> ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sdtmndtasgtdt0(xc,xR,X4)
& ( ( sdtmndtplgtdt0(xc,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xc,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xc,xR) ) )
| xc = X4 )
& sdtmndtasgtdt0(xb,xR,X4)
& ( ( sdtmndtplgtdt0(xb,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xb,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xb,xR) ) )
| xb = X4 )
& aNormalFormOfIn0(X4,X3,xR)
& ~ ? [X5] : aReductOfIn0(X5,X4,xR)
& sdtmndtasgtdt0(X3,xR,X4)
& ( ( sdtmndtplgtdt0(X3,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,X3,xR)
& aElement0(X5) )
| aReductOfIn0(X4,X3,xR) ) )
| X3 = X4 )
& aElement0(X4) )
& sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) )
& sdtmndtasgtdt0(X2,xR,xc)
& ( ( sdtmndtplgtdt0(X2,xR,xc)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,xc)
& aReductOfIn0(X3,X2,xR)
& aElement0(X3) )
| aReductOfIn0(xc,X2,xR) ) )
| X2 = xc )
& aReductOfIn0(X2,xa,xR)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xb)
& ( ( sdtmndtplgtdt0(X1,xR,xb)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,xb)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
| aReductOfIn0(xb,X1,xR) ) )
| X1 = xb )
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) ) ),
introduced(definition) ).
fof(c_0_4,negated_conjecture,
~ ( ( ( ( sdtmndtplgtdt0(xa,xR,xc)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xc,xa,xR) )
& ( sdtmndtplgtdt0(xa,xR,xb)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,xb)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xb,xa,xR) ) )
=> epred1_0 )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& ( ( sdtmndtplgtdt0(xa,xR,xc)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xc,xa,xR) ) )
| xa = xc )
& sdtmndtasgtdt0(xa,xR,xb)
& ( ( sdtmndtplgtdt0(xa,xR,xb)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xb)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
| aReductOfIn0(xb,xa,xR) ) )
| xa = xb ) )
=> ? [X1] :
( ( sdtmndtasgtdt0(xc,xR,X1)
| sdtmndtplgtdt0(xc,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xc,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xc,xR)
| xc = X1 )
& ( sdtmndtasgtdt0(xb,xR,X1)
| sdtmndtplgtdt0(xb,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,xb,xR)
& aElement0(X2) )
| aReductOfIn0(X1,xb,xR)
| xb = X1 )
& aElement0(X1) ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
fof(c_0_5,plain,
( epred1_0
=> ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sdtmndtasgtdt0(xc,xR,X4)
& ( ( sdtmndtplgtdt0(xc,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xc,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xc,xR) ) )
| xc = X4 )
& sdtmndtasgtdt0(xb,xR,X4)
& ( ( sdtmndtplgtdt0(xb,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,xb,xR)
& aElement0(X5) )
| aReductOfIn0(X4,xb,xR) ) )
| xb = X4 )
& aNormalFormOfIn0(X4,X3,xR)
& ~ ? [X5] : aReductOfIn0(X5,X4,xR)
& sdtmndtasgtdt0(X3,xR,X4)
& ( ( sdtmndtplgtdt0(X3,xR,X4)
& ( ? [X5] :
( sdtmndtplgtdt0(X5,xR,X4)
& aReductOfIn0(X5,X3,xR)
& aElement0(X5) )
| aReductOfIn0(X4,X3,xR) ) )
| X3 = X4 )
& aElement0(X4) )
& sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) )
& sdtmndtasgtdt0(X2,xR,xc)
& ( ( sdtmndtplgtdt0(X2,xR,xc)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,xc)
& aReductOfIn0(X3,X2,xR)
& aElement0(X3) )
| aReductOfIn0(xc,X2,xR) ) )
| X2 = xc )
& aReductOfIn0(X2,xa,xR)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xb)
& ( ( sdtmndtplgtdt0(X1,xR,xb)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,xb)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
| aReductOfIn0(xb,X1,xR) ) )
| X1 = xb )
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) ) ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
fof(c_0_6,negated_conjecture,
! [X81,X82,X85,X86,X87] :
( ( ~ aElement0(X85)
| ~ sdtmndtasgtdt0(xb,xR,X85)
| ~ sdtmndtasgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ sdtmndtasgtdt0(xb,xR,X85)
| ~ sdtmndtplgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ sdtmndtasgtdt0(xb,xR,X85)
| ~ sdtmndtplgtdt0(X87,xR,X85)
| ~ aReductOfIn0(X87,xc,xR)
| ~ aElement0(X87) )
& ( ~ aElement0(X85)
| ~ sdtmndtasgtdt0(xb,xR,X85)
| ~ aReductOfIn0(X85,xc,xR) )
& ( ~ aElement0(X85)
| ~ sdtmndtasgtdt0(xb,xR,X85)
| xc != X85 )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(xb,xR,X85)
| ~ sdtmndtasgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(xb,xR,X85)
| ~ sdtmndtplgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(xb,xR,X85)
| ~ sdtmndtplgtdt0(X87,xR,X85)
| ~ aReductOfIn0(X87,xc,xR)
| ~ aElement0(X87) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(xb,xR,X85)
| ~ aReductOfIn0(X85,xc,xR) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(xb,xR,X85)
| xc != X85 )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(X86,xR,X85)
| ~ aReductOfIn0(X86,xb,xR)
| ~ aElement0(X86)
| ~ sdtmndtasgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(X86,xR,X85)
| ~ aReductOfIn0(X86,xb,xR)
| ~ aElement0(X86)
| ~ sdtmndtplgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(X86,xR,X85)
| ~ aReductOfIn0(X86,xb,xR)
| ~ aElement0(X86)
| ~ sdtmndtplgtdt0(X87,xR,X85)
| ~ aReductOfIn0(X87,xc,xR)
| ~ aElement0(X87) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(X86,xR,X85)
| ~ aReductOfIn0(X86,xb,xR)
| ~ aElement0(X86)
| ~ aReductOfIn0(X85,xc,xR) )
& ( ~ aElement0(X85)
| ~ sdtmndtplgtdt0(X86,xR,X85)
| ~ aReductOfIn0(X86,xb,xR)
| ~ aElement0(X86)
| xc != X85 )
& ( ~ aElement0(X85)
| ~ aReductOfIn0(X85,xb,xR)
| ~ sdtmndtasgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ aReductOfIn0(X85,xb,xR)
| ~ sdtmndtplgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| ~ aReductOfIn0(X85,xb,xR)
| ~ sdtmndtplgtdt0(X87,xR,X85)
| ~ aReductOfIn0(X87,xc,xR)
| ~ aElement0(X87) )
& ( ~ aElement0(X85)
| ~ aReductOfIn0(X85,xb,xR)
| ~ aReductOfIn0(X85,xc,xR) )
& ( ~ aElement0(X85)
| ~ aReductOfIn0(X85,xb,xR)
| xc != X85 )
& ( ~ aElement0(X85)
| xb != X85
| ~ sdtmndtasgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| xb != X85
| ~ sdtmndtplgtdt0(xc,xR,X85) )
& ( ~ aElement0(X85)
| xb != X85
| ~ sdtmndtplgtdt0(X87,xR,X85)
| ~ aReductOfIn0(X87,xc,xR)
| ~ aElement0(X87) )
& ( ~ aElement0(X85)
| xb != X85
| ~ aReductOfIn0(X85,xc,xR) )
& ( ~ aElement0(X85)
| xb != X85
| xc != X85 )
& sdtmndtasgtdt0(xa,xR,xc)
& ( xa = xc
| sdtmndtplgtdt0(xa,xR,xc) )
& ( xa = xc
| aReductOfIn0(xc,xa,xR)
| sdtmndtplgtdt0(esk21_0,xR,xc) )
& ( xa = xc
| aReductOfIn0(xc,xa,xR)
| aReductOfIn0(esk21_0,xa,xR) )
& ( xa = xc
| aReductOfIn0(xc,xa,xR)
| aElement0(esk21_0) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xb
| sdtmndtplgtdt0(xa,xR,xb) )
& ( xa = xb
| aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(esk20_0,xR,xb) )
& ( xa = xb
| aReductOfIn0(xb,xa,xR)
| aReductOfIn0(esk20_0,xa,xR) )
& ( xa = xb
| aReductOfIn0(xb,xa,xR)
| aElement0(esk20_0) )
& ( epred1_0
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( epred1_0
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(X82,xR,xc)
| ~ aReductOfIn0(X82,xa,xR)
| ~ aElement0(X82) )
& ( epred1_0
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aReductOfIn0(xc,xa,xR) )
& ( epred1_0
| ~ sdtmndtplgtdt0(X81,xR,xb)
| ~ aReductOfIn0(X81,xa,xR)
| ~ aElement0(X81)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( epred1_0
| ~ sdtmndtplgtdt0(X81,xR,xb)
| ~ aReductOfIn0(X81,xa,xR)
| ~ aElement0(X81)
| ~ sdtmndtplgtdt0(X82,xR,xc)
| ~ aReductOfIn0(X82,xa,xR)
| ~ aElement0(X82) )
& ( epred1_0
| ~ sdtmndtplgtdt0(X81,xR,xb)
| ~ aReductOfIn0(X81,xa,xR)
| ~ aElement0(X81)
| ~ aReductOfIn0(xc,xa,xR) )
& ( epred1_0
| ~ aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( epred1_0
| ~ aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(X82,xR,xc)
| ~ aReductOfIn0(X82,xa,xR)
| ~ aElement0(X82) )
& ( epred1_0
| ~ aReductOfIn0(xb,xa,xR)
| ~ aReductOfIn0(xc,xa,xR) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
fof(c_0_7,plain,
! [X97] :
( ( ~ epred1_0
| sdtmndtasgtdt0(xc,xR,esk29_0) )
& ( ~ epred1_0
| xc = esk29_0
| sdtmndtplgtdt0(xc,xR,esk29_0) )
& ( ~ epred1_0
| xc = esk29_0
| aReductOfIn0(esk29_0,xc,xR)
| sdtmndtplgtdt0(esk32_0,xR,esk29_0) )
& ( ~ epred1_0
| xc = esk29_0
| aReductOfIn0(esk29_0,xc,xR)
| aReductOfIn0(esk32_0,xc,xR) )
& ( ~ epred1_0
| xc = esk29_0
| aReductOfIn0(esk29_0,xc,xR)
| aElement0(esk32_0) )
& ( ~ epred1_0
| sdtmndtasgtdt0(xb,xR,esk29_0) )
& ( ~ epred1_0
| xb = esk29_0
| sdtmndtplgtdt0(xb,xR,esk29_0) )
& ( ~ epred1_0
| xb = esk29_0
| aReductOfIn0(esk29_0,xb,xR)
| sdtmndtplgtdt0(esk31_0,xR,esk29_0) )
& ( ~ epred1_0
| xb = esk29_0
| aReductOfIn0(esk29_0,xb,xR)
| aReductOfIn0(esk31_0,xb,xR) )
& ( ~ epred1_0
| xb = esk29_0
| aReductOfIn0(esk29_0,xb,xR)
| aElement0(esk31_0) )
& ( ~ epred1_0
| aNormalFormOfIn0(esk29_0,esk26_0,xR) )
& ( ~ epred1_0
| ~ aReductOfIn0(X97,esk29_0,xR) )
& ( ~ epred1_0
| sdtmndtasgtdt0(esk26_0,xR,esk29_0) )
& ( ~ epred1_0
| esk26_0 = esk29_0
| sdtmndtplgtdt0(esk26_0,xR,esk29_0) )
& ( ~ epred1_0
| esk26_0 = esk29_0
| aReductOfIn0(esk29_0,esk26_0,xR)
| sdtmndtplgtdt0(esk30_0,xR,esk29_0) )
& ( ~ epred1_0
| esk26_0 = esk29_0
| aReductOfIn0(esk29_0,esk26_0,xR)
| aReductOfIn0(esk30_0,esk26_0,xR) )
& ( ~ epred1_0
| esk26_0 = esk29_0
| aReductOfIn0(esk29_0,esk26_0,xR)
| aElement0(esk30_0) )
& ( ~ epred1_0
| aElement0(esk29_0) )
& ( ~ epred1_0
| sdtmndtasgtdt0(esk24_0,xR,esk26_0) )
& ( ~ epred1_0
| esk24_0 = esk26_0
| sdtmndtplgtdt0(esk24_0,xR,esk26_0) )
& ( ~ epred1_0
| esk24_0 = esk26_0
| aReductOfIn0(esk26_0,esk24_0,xR)
| sdtmndtplgtdt0(esk28_0,xR,esk26_0) )
& ( ~ epred1_0
| esk24_0 = esk26_0
| aReductOfIn0(esk26_0,esk24_0,xR)
| aReductOfIn0(esk28_0,esk24_0,xR) )
& ( ~ epred1_0
| esk24_0 = esk26_0
| aReductOfIn0(esk26_0,esk24_0,xR)
| aElement0(esk28_0) )
& ( ~ epred1_0
| sdtmndtasgtdt0(esk22_0,xR,esk26_0) )
& ( ~ epred1_0
| esk22_0 = esk26_0
| sdtmndtplgtdt0(esk22_0,xR,esk26_0) )
& ( ~ epred1_0
| esk22_0 = esk26_0
| aReductOfIn0(esk26_0,esk22_0,xR)
| sdtmndtplgtdt0(esk27_0,xR,esk26_0) )
& ( ~ epred1_0
| esk22_0 = esk26_0
| aReductOfIn0(esk26_0,esk22_0,xR)
| aReductOfIn0(esk27_0,esk22_0,xR) )
& ( ~ epred1_0
| esk22_0 = esk26_0
| aReductOfIn0(esk26_0,esk22_0,xR)
| aElement0(esk27_0) )
& ( ~ epred1_0
| aElement0(esk26_0) )
& ( ~ epred1_0
| sdtmndtasgtdt0(esk24_0,xR,xc) )
& ( ~ epred1_0
| esk24_0 = xc
| sdtmndtplgtdt0(esk24_0,xR,xc) )
& ( ~ epred1_0
| esk24_0 = xc
| aReductOfIn0(xc,esk24_0,xR)
| sdtmndtplgtdt0(esk25_0,xR,xc) )
& ( ~ epred1_0
| esk24_0 = xc
| aReductOfIn0(xc,esk24_0,xR)
| aReductOfIn0(esk25_0,esk24_0,xR) )
& ( ~ epred1_0
| esk24_0 = xc
| aReductOfIn0(xc,esk24_0,xR)
| aElement0(esk25_0) )
& ( ~ epred1_0
| aReductOfIn0(esk24_0,xa,xR) )
& ( ~ epred1_0
| aElement0(esk24_0) )
& ( ~ epred1_0
| sdtmndtasgtdt0(esk22_0,xR,xb) )
& ( ~ epred1_0
| esk22_0 = xb
| sdtmndtplgtdt0(esk22_0,xR,xb) )
& ( ~ epred1_0
| esk22_0 = xb
| aReductOfIn0(xb,esk22_0,xR)
| sdtmndtplgtdt0(esk23_0,xR,xb) )
& ( ~ epred1_0
| esk22_0 = xb
| aReductOfIn0(xb,esk22_0,xR)
| aReductOfIn0(esk23_0,esk22_0,xR) )
& ( ~ epred1_0
| esk22_0 = xb
| aReductOfIn0(xb,esk22_0,xR)
| aElement0(esk23_0) )
& ( ~ epred1_0
| aReductOfIn0(esk22_0,xa,xR) )
& ( ~ epred1_0
| aElement0(esk22_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
cnf(c_0_8,negated_conjecture,
( ~ aElement0(X1)
| ~ sdtmndtplgtdt0(xb,xR,X1)
| ~ sdtmndtasgtdt0(xc,xR,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ epred1_0
| sdtmndtasgtdt0(xc,xR,esk29_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ epred1_0
| aElement0(esk29_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( ~ sdtmndtplgtdt0(xb,xR,esk29_0)
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_14,plain,
( ~ epred1_0
| xb = esk29_0
| sdtmndtplgtdt0(xb,xR,esk29_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( ~ aElement0(X1)
| xb != X1
| ~ sdtmndtasgtdt0(xc,xR,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__731]) ).
cnf(c_0_17,negated_conjecture,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| epred1_0
| xc = xa ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,plain,
( ~ epred1_0
| esk29_0 = xb ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ sdtmndtasgtdt0(xc,xR,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16])]) ).
cnf(c_0_21,negated_conjecture,
( epred1_0
| xc = xa
| xb = xa ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
~ epred1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( ~ aElement0(X1)
| ~ sdtmndtasgtdt0(xb,xR,X1)
| xc != X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__731]) ).
cnf(c_0_25,negated_conjecture,
( xb = xa
| xc = xa ),
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xb),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
xb = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xc),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM022+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 14:18:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.44 % Version: 3.5.1
% 0.09/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.44 % Starting sh5l with 300s (1) cores
% 0.09/0.44 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1672268 completed with status 0
% 0.09/0.44 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.09/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.44 % No SInE strategy applied
% 0.09/0.44 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.09/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.09/0.44 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.09/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.44 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.09/0.44 % SubtermCWHack with pid 1672272 completed with status 0
% 0.09/0.44 % Result found by SubtermCWHack
% 0.09/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.44 % No SInE strategy applied
% 0.09/0.44 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.09/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.44 % Preprocessing time : 0.006 s
% 0.09/0.44
% 0.09/0.44 % Proof found!
% 0.09/0.44 % SZS status Theorem
% 0.09/0.44 % SZS output start CNFRefutation
% See solution above
% 0.09/0.44 % Parsed axioms : 19
% 0.09/0.44 % Removed by relevancy pruning/SinE : 0
% 0.09/0.44 % Initial clauses : 425
% 0.09/0.44 % Removed in clause preprocessing : 4
% 0.09/0.44 % Initial clauses in saturation : 421
% 0.09/0.44 % Processed clauses : 111
% 0.09/0.44 % ...of these trivial : 0
% 0.09/0.44 % ...subsumed : 11
% 0.09/0.44 % ...remaining for further processing : 100
% 0.09/0.44 % Other redundant clauses eliminated : 8
% 0.09/0.44 % Clauses deleted for lack of memory : 0
% 0.09/0.44 % Backward-subsumed : 35
% 0.09/0.44 % Backward-rewritten : 28
% 0.09/0.44 % Generated clauses : 75
% 0.09/0.44 % ...of the previous two non-redundant : 79
% 0.09/0.44 % ...aggressively subsumed : 0
% 0.09/0.44 % Contextual simplify-reflections : 3
% 0.09/0.44 % Paramodulations : 66
% 0.09/0.44 % Factorizations : 0
% 0.09/0.44 % NegExts : 0
% 0.09/0.44 % Equation resolutions : 8
% 0.09/0.44 % Disequality decompositions : 0
% 0.09/0.44 % Total rewrite steps : 56
% 0.09/0.44 % ...of those cached : 49
% 0.09/0.44 % Propositional unsat checks : 0
% 0.09/0.44 % Propositional check models : 0
% 0.09/0.44 % Propositional check unsatisfiable : 0
% 0.09/0.44 % Propositional clauses : 0
% 0.09/0.44 % Propositional clauses after purity: 0
% 0.09/0.44 % Propositional unsat core size : 0
% 0.09/0.44 % Propositional preprocessing time : 0.000
% 0.09/0.44 % Propositional encoding time : 0.000
% 0.09/0.44 % Propositional solver time : 0.000
% 0.09/0.44 % Success case prop preproc time : 0.000
% 0.09/0.44 % Success case prop encoding time : 0.000
% 0.09/0.44 % Success case prop solver time : 0.000
% 0.09/0.44 % Current number of processed clauses : 28
% 0.09/0.44 % Positive orientable unit clauses : 7
% 0.09/0.44 % Positive unorientable unit clauses: 0
% 0.09/0.44 % Negative unit clauses : 1
% 0.09/0.44 % Non-unit-clauses : 20
% 0.09/0.44 % Current number of unprocessed clauses: 370
% 0.09/0.44 % ...number of literals in the above : 2962
% 0.09/0.44 % Current number of archived formulas : 0
% 0.09/0.44 % Current number of archived clauses : 64
% 0.09/0.44 % Clause-clause subsumption calls (NU) : 811
% 0.09/0.44 % Rec. Clause-clause subsumption calls : 613
% 0.09/0.44 % Non-unit clause-clause subsumptions : 15
% 0.09/0.44 % Unit Clause-clause subsumption calls : 88
% 0.09/0.44 % Rewrite failures with RHS unbound : 0
% 0.09/0.44 % BW rewrite match attempts : 2
% 0.09/0.44 % BW rewrite match successes : 1
% 0.09/0.44 % Condensation attempts : 0
% 0.09/0.44 % Condensation successes : 0
% 0.09/0.44 % Termbank termtop insertions : 25304
% 0.09/0.44 % Search garbage collected termcells : 3107
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.021 s
% 0.09/0.44 % System time : 0.003 s
% 0.09/0.44 % Total time : 0.025 s
% 0.09/0.44 % Maximum resident set size: 4404 pages
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.072 s
% 0.09/0.44 % System time : 0.016 s
% 0.09/0.44 % Total time : 0.088 s
% 0.09/0.44 % Maximum resident set size: 4608 pages
% 0.09/0.44 % E exiting
%------------------------------------------------------------------------------