%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG106+2 : 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 : n020.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 02:06:25 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 413 ( 95 equ)
% Maximal formula atoms : 258 ( 11 avg)
% Number of connectives : 624 ( 246 ~; 254 |; 103 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 68 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 71 ( 4 sgn 39 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ! [X1,X2,X3] :
( ( aElement0(X3)
& ( aElementOf0(X2,slsdtgt0(xc))
| ? [X4] :
( sdtasdt0(xc,X4) = X2
& aElement0(X4) ) )
& ( aElementOf0(X1,slsdtgt0(xc))
| ? [X4] :
( sdtasdt0(xc,X4) = X1
& aElement0(X4) ) ) )
=> ? [X4] :
( ? [X5] :
( aElementOf0(sdtasdt0(X3,X1),slsdtgt0(xc))
& ? [X6] :
( sdtasdt0(xc,X6) = sdtasdt0(X3,X1)
& aElement0(X6) )
& aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc))
& ? [X6] :
( sdtasdt0(xc,X6) = sdtpldt0(X1,X2)
& aElement0(X6) )
& sdtasdt0(X3,X1) = sdtasdt0(xc,sdtasdt0(X4,X3))
& sdtpldt0(X1,X2) = sdtasdt0(xc,sdtpldt0(X4,X5))
& sdtasdt0(xc,X5) = X2
& aElement0(X5) )
& sdtasdt0(xc,X4) = X1
& aElement0(X4) ) )
=> ( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
<=> ? [X2] :
( sdtasdt0(xc,X2) = X1
& aElement0(X2) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc)) )
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) )
& ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) ) ) )
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_4,negated_conjecture,
~ ( ! [X1,X2,X3] :
( ( aElement0(X3)
& ( aElementOf0(X2,slsdtgt0(xc))
| ? [X4] :
( sdtasdt0(xc,X4) = X2
& aElement0(X4) ) )
& ( aElementOf0(X1,slsdtgt0(xc))
| ? [X4] :
( sdtasdt0(xc,X4) = X1
& aElement0(X4) ) ) )
=> ? [X4] :
( ? [X5] :
( aElementOf0(sdtasdt0(X3,X1),slsdtgt0(xc))
& ? [X6] :
( sdtasdt0(xc,X6) = sdtasdt0(X3,X1)
& aElement0(X6) )
& aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc))
& ? [X6] :
( sdtasdt0(xc,X6) = sdtpldt0(X1,X2)
& aElement0(X6) )
& sdtasdt0(X3,X1) = sdtasdt0(xc,sdtasdt0(X4,X3))
& sdtpldt0(X1,X2) = sdtasdt0(xc,sdtpldt0(X4,X5))
& sdtasdt0(xc,X5) = X2
& aElement0(X5) )
& sdtasdt0(xc,X4) = X1
& aElement0(X4) ) )
=> ( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
<=> ? [X2] :
( sdtasdt0(xc,X2) = X1
& aElement0(X2) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc)) )
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,negated_conjecture,
! [X115,X116,X117,X118,X119,X124,X126,X127] :
( ~ aIdeal0(slsdtgt0(xc))
& ( ~ aElementOf0(sdtpldt0(esk26_0,esk27_0),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(esk28_0,esk26_0),slsdtgt0(xc)) )
& ( ~ aElementOf0(sdtpldt0(esk26_0,esk27_0),slsdtgt0(xc))
| aElement0(esk28_0) )
& ( aElementOf0(esk27_0,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(esk28_0,esk26_0),slsdtgt0(xc)) )
& ( aElementOf0(esk27_0,slsdtgt0(xc))
| aElement0(esk28_0) )
& aElementOf0(esk26_0,slsdtgt0(xc))
& ( aElementOf0(X126,slsdtgt0(xc))
| sdtasdt0(xc,X127) != X126
| ~ aElement0(X127) )
& ( ~ aElementOf0(X124,slsdtgt0(xc))
| sdtasdt0(xc,esk25_1(X124)) = X124 )
& ( ~ aElementOf0(X124,slsdtgt0(xc))
| aElement0(esk25_1(X124)) )
& aSet0(slsdtgt0(xc))
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X117,X115),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk24_3(X115,X116,X117)) = sdtasdt0(X117,X115) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk24_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X115,X116),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk23_3(X115,X116,X117)) = sdtpldt0(X115,X116) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk23_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(X117,X115) = sdtasdt0(xc,sdtasdt0(esk21_3(X115,X116,X117),X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtpldt0(X115,X116) = sdtasdt0(xc,sdtpldt0(esk21_3(X115,X116,X117),esk22_3(X115,X116,X117))) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk22_3(X115,X116,X117)) = X116 )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk22_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk21_3(X115,X116,X117)) = X115 )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk21_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElementOf0(sdtasdt0(X117,X115),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk24_3(X115,X116,X117)) = sdtasdt0(X117,X115) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk24_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElementOf0(sdtpldt0(X115,X116),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk23_3(X115,X116,X117)) = sdtpldt0(X115,X116) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk23_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(X117,X115) = sdtasdt0(xc,sdtasdt0(esk21_3(X115,X116,X117),X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtpldt0(X115,X116) = sdtasdt0(xc,sdtpldt0(esk21_3(X115,X116,X117),esk22_3(X115,X116,X117))) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk22_3(X115,X116,X117)) = X116 )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk22_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk21_3(X115,X116,X117)) = X115 )
& ( ~ aElement0(X117)
| ~ aElementOf0(X115,slsdtgt0(xc))
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk21_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X117,X115),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk24_3(X115,X116,X117)) = sdtasdt0(X117,X115) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk24_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X115,X116),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk23_3(X115,X116,X117)) = sdtpldt0(X115,X116) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk23_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(X117,X115) = sdtasdt0(xc,sdtasdt0(esk21_3(X115,X116,X117),X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtpldt0(X115,X116) = sdtasdt0(xc,sdtpldt0(esk21_3(X115,X116,X117),esk22_3(X115,X116,X117))) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk22_3(X115,X116,X117)) = X116 )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk22_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| sdtasdt0(xc,esk21_3(X115,X116,X117)) = X115 )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| ~ aElementOf0(X116,slsdtgt0(xc))
| aElement0(esk21_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElementOf0(sdtasdt0(X117,X115),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk24_3(X115,X116,X117)) = sdtasdt0(X117,X115) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk24_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElementOf0(sdtpldt0(X115,X116),slsdtgt0(xc)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk23_3(X115,X116,X117)) = sdtpldt0(X115,X116) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk23_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(X117,X115) = sdtasdt0(xc,sdtasdt0(esk21_3(X115,X116,X117),X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtpldt0(X115,X116) = sdtasdt0(xc,sdtpldt0(esk21_3(X115,X116,X117),esk22_3(X115,X116,X117))) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk22_3(X115,X116,X117)) = X116 )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk22_3(X115,X116,X117)) )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| sdtasdt0(xc,esk21_3(X115,X116,X117)) = X115 )
& ( ~ aElement0(X117)
| sdtasdt0(xc,X118) != X115
| ~ aElement0(X118)
| sdtasdt0(xc,X119) != X116
| ~ aElement0(X119)
| aElement0(esk21_3(X115,X116,X117)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])])]) ).
fof(c_0_6,plain,
! [X62,X63,X64,X65,X66] :
( ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk9_1(X66),X66) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtasdt0(X65,X63),X62)
| ~ aElement0(X65) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtpldt0(X63,X64),X62)
| ~ aElementOf0(X64,X62) )
& ( ~ aIdeal0(X62)
| aSet0(X62) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefIdeal])])])])])])]) ).
cnf(c_0_7,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(xc))
| ~ aElementOf0(X3,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ aSet0(X1)
| aIdeal0(X1)
| aElementOf0(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
aSet0(slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
~ aIdeal0(slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),c_0_10]) ).
cnf(c_0_12,negated_conjecture,
aElementOf0(esk26_0,slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( ~ aElement0(X3)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X1,X2),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( ~ aElementOf0(sdtasdt0(esk28_0,esk26_0),slsdtgt0(xc))
| aElementOf0(esk27_0,slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,esk26_0),slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( aElementOf0(esk27_0,slsdtgt0(xc))
| aElement0(esk28_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X1,esk26_0),slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
aElementOf0(esk27_0,slsdtgt0(xc)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xc))
| aElement0(esk25_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_20,plain,
! [X34,X35] :
( aElement0(X35)
| ~ aElementOf0(X35,X34)
| ~ aSet0(X34) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ aElement0(X1)
| aElementOf0(sdtpldt0(esk27_0,esk26_0),slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
aElement0(esk25_1(esk27_0)),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
fof(c_0_23,plain,
! [X13,X14] :
( sdtpldt0(X13,X14) = sdtpldt0(X14,X13)
| ~ aElement0(X14)
| ~ aElement0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_24,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
aElementOf0(sdtpldt0(esk27_0,esk26_0),slsdtgt0(xc)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
aElement0(esk26_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_12]),c_0_9])]) ).
cnf(c_0_28,negated_conjecture,
aElement0(esk27_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_9])]) ).
cnf(c_0_29,negated_conjecture,
( ~ aElementOf0(sdtpldt0(esk26_0,esk27_0),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(esk28_0,esk26_0),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_30,negated_conjecture,
aElementOf0(sdtpldt0(esk26_0,esk27_0),slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
( ~ aElementOf0(sdtpldt0(esk26_0,esk27_0),slsdtgt0(xc))
| aElement0(esk28_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_32,negated_conjecture,
~ aElementOf0(sdtasdt0(esk28_0,esk26_0),slsdtgt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
aElement0(esk28_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_30])]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_15]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG106+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:21:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.16/0.50 % Version: 3.5.1
% 0.16/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.50 % Starting sh5l with 300s (1) cores
% 0.16/0.50 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1988998 completed with status 0
% 0.16/0.50 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.50 % No SInE strategy applied
% 0.16/0.50 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.16/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.50 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.16/0.50 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 0.16/0.50 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1989009 completed with status 0
% 0.16/0.50 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.50 % No SInE strategy applied
% 0.16/0.50 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.16/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.50 % Preprocessing time : 0.002 s
% 0.16/0.50 % Presaturation interreduction done
% 0.16/0.50
% 0.16/0.50 % Proof found!
% 0.16/0.50 % SZS status Theorem
% 0.16/0.50 % SZS output start CNFRefutation
% See solution above
% 0.16/0.51 % Parsed axioms : 39
% 0.16/0.51 % Removed by relevancy pruning/SinE : 0
% 0.16/0.51 % Initial clauses : 151
% 0.16/0.51 % Removed in clause preprocessing : 4
% 0.16/0.51 % Initial clauses in saturation : 147
% 0.16/0.51 % Processed clauses : 587
% 0.16/0.51 % ...of these trivial : 15
% 0.16/0.51 % ...subsumed : 66
% 0.16/0.51 % ...remaining for further processing : 506
% 0.16/0.51 % Other redundant clauses eliminated : 65
% 0.16/0.51 % Clauses deleted for lack of memory : 0
% 0.16/0.51 % Backward-subsumed : 6
% 0.16/0.51 % Backward-rewritten : 10
% 0.16/0.51 % Generated clauses : 3793
% 0.16/0.51 % ...of the previous two non-redundant : 3584
% 0.16/0.51 % ...aggressively subsumed : 0
% 0.16/0.51 % Contextual simplify-reflections : 2
% 0.16/0.51 % Paramodulations : 3738
% 0.16/0.51 % Factorizations : 4
% 0.16/0.51 % NegExts : 0
% 0.16/0.51 % Equation resolutions : 65
% 0.16/0.51 % Disequality decompositions : 0
% 0.16/0.51 % Total rewrite steps : 2479
% 0.16/0.51 % ...of those cached : 2421
% 0.16/0.51 % Propositional unsat checks : 0
% 0.16/0.51 % Propositional check models : 0
% 0.16/0.51 % Propositional check unsatisfiable : 0
% 0.16/0.51 % Propositional clauses : 0
% 0.16/0.51 % Propositional clauses after purity: 0
% 0.16/0.51 % Propositional unsat core size : 0
% 0.16/0.51 % Propositional preprocessing time : 0.000
% 0.16/0.51 % Propositional encoding time : 0.000
% 0.16/0.51 % Propositional solver time : 0.000
% 0.16/0.51 % Success case prop preproc time : 0.000
% 0.16/0.51 % Success case prop encoding time : 0.000
% 0.16/0.51 % Success case prop solver time : 0.000
% 0.16/0.51 % Current number of processed clauses : 292
% 0.16/0.51 % Positive orientable unit clauses : 82
% 0.16/0.51 % Positive unorientable unit clauses: 0
% 0.16/0.51 % Negative unit clauses : 3
% 0.16/0.51 % Non-unit-clauses : 207
% 0.16/0.51 % Current number of unprocessed clauses: 3222
% 0.16/0.51 % ...number of literals in the above : 14174
% 0.16/0.51 % Current number of archived formulas : 0
% 0.16/0.51 % Current number of archived clauses : 163
% 0.16/0.51 % Clause-clause subsumption calls (NU) : 13164
% 0.16/0.51 % Rec. Clause-clause subsumption calls : 6641
% 0.16/0.51 % Non-unit clause-clause subsumptions : 63
% 0.16/0.51 % Unit Clause-clause subsumption calls : 855
% 0.16/0.51 % Rewrite failures with RHS unbound : 0
% 0.16/0.51 % BW rewrite match attempts : 40
% 0.16/0.51 % BW rewrite match successes : 12
% 0.16/0.51 % Condensation attempts : 0
% 0.16/0.51 % Condensation successes : 0
% 0.16/0.51 % Termbank termtop insertions : 77931
% 0.16/0.51 % Search garbage collected termcells : 2414
% 0.16/0.51
% 0.16/0.51 % -------------------------------------------------
% 0.16/0.51 % User time : 0.058 s
% 0.16/0.51 % System time : 0.007 s
% 0.16/0.51 % Total time : 0.065 s
% 0.16/0.51 % Maximum resident set size: 3948 pages
% 0.16/0.51
% 0.16/0.51 % -------------------------------------------------
% 0.16/0.51 % User time : 0.194 s
% 0.16/0.51 % System time : 0.023 s
% 0.16/0.51 % Total time : 0.217 s
% 0.16/0.51 % Maximum resident set size: 4608 pages
% 0.16/0.51 % E exiting
%------------------------------------------------------------------------------