%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG086+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:16 PM UTC 2026
% Result : Theorem 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 151 ( 25 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 207 ( 82 ~; 90 |; 28 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn 25 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( aElementOf0(X5,X1)
& aElementOf0(X6,X2)
& sdtpldt0(X5,X6) = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__,conjecture,
? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xx = sdtpldt0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(m__901,hypothesis,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(c_0_5,plain,
! [X87,X88,X89,X90,X93,X94,X95,X96,X98,X99] :
( ( aSet0(X89)
| X89 != sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( aElementOf0(esk3_4(X87,X88,X89,X90),X87)
| ~ aElementOf0(X90,X89)
| X89 != sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( aElementOf0(esk4_4(X87,X88,X89,X90),X88)
| ~ aElementOf0(X90,X89)
| X89 != sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( sdtpldt0(esk3_4(X87,X88,X89,X90),esk4_4(X87,X88,X89,X90)) = X90
| ~ aElementOf0(X90,X89)
| X89 != sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( ~ aElementOf0(X94,X87)
| ~ aElementOf0(X95,X88)
| sdtpldt0(X94,X95) != X93
| aElementOf0(X93,X89)
| X89 != sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( ~ aElementOf0(esk5_3(X87,X88,X96),X96)
| ~ aElementOf0(X98,X87)
| ~ aElementOf0(X99,X88)
| sdtpldt0(X98,X99) != esk5_3(X87,X88,X96)
| ~ aSet0(X96)
| X96 = sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( aElementOf0(esk6_3(X87,X88,X96),X87)
| aElementOf0(esk5_3(X87,X88,X96),X96)
| ~ aSet0(X96)
| X96 = sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( aElementOf0(esk7_3(X87,X88,X96),X88)
| aElementOf0(esk5_3(X87,X88,X96),X96)
| ~ aSet0(X96)
| X96 = sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) )
& ( sdtpldt0(esk6_3(X87,X88,X96),esk7_3(X87,X88,X96)) = esk5_3(X87,X88,X96)
| aElementOf0(esk5_3(X87,X88,X96),X96)
| ~ aSet0(X96)
| X96 = sdtpldt1(X87,X88)
| ~ aSet0(X87)
| ~ aSet0(X88) ) ),
inference(distribute,[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)],[mDefSSum])])])])])]) ).
fof(c_0_6,plain,
! [X109,X110,X111,X112,X113] :
( ( aSet0(X109)
| ~ aIdeal0(X109) )
& ( ~ aElementOf0(X111,X109)
| aElementOf0(sdtpldt0(X110,X111),X109)
| ~ aElementOf0(X110,X109)
| ~ aIdeal0(X109) )
& ( ~ aElement0(X112)
| aElementOf0(sdtasdt0(X112,X110),X109)
| ~ aElementOf0(X110,X109)
| ~ aIdeal0(X109) )
& ( aElementOf0(esk9_1(X113),X113)
| ~ aSet0(X113)
| aIdeal0(X113) )
& ( aElement0(esk11_1(X113))
| aElementOf0(esk10_1(X113),X113)
| ~ aSet0(X113)
| aIdeal0(X113) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X113),esk9_1(X113)),X113)
| aElementOf0(esk10_1(X113),X113)
| ~ aSet0(X113)
| aIdeal0(X113) )
& ( aElement0(esk11_1(X113))
| ~ aElementOf0(sdtpldt0(esk9_1(X113),esk10_1(X113)),X113)
| ~ aSet0(X113)
| aIdeal0(X113) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X113),esk9_1(X113)),X113)
| ~ aElementOf0(sdtpldt0(esk9_1(X113),esk10_1(X113)),X113)
| ~ aSet0(X113)
| aIdeal0(X113) ) ),
inference(distribute,[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])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xx = sdtpldt0(X1,X2) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_8,plain,
( sdtpldt0(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4)) = X4
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_11,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_12,plain,
( aElementOf0(esk4_4(X1,X2,X3,X4),X2)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( aElementOf0(esk3_4(X1,X2,X3,X4),X1)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,negated_conjecture,
! [X117,X118] :
( ~ aElementOf0(X117,xI)
| ~ aElementOf0(X118,xJ)
| xx != sdtpldt0(X117,X118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_15,plain,
( sdtpldt0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),esk4_4(X1,X2,sdtpldt1(X1,X2),X3)) = X3
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[m__901]) ).
cnf(c_0_17,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_18,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_19,plain,
( aElementOf0(esk4_4(X1,X2,sdtpldt1(X1,X2),X3),X2)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( aElementOf0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),X1)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xJ)
| xx != sdtpldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xx),esk4_4(xI,xJ,sdtpldt1(xI,xJ),xx)) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_23,hypothesis,
aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),xx),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_24,hypothesis,
aElementOf0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xx),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG086+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n028.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:50:16 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Theorem for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------