%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG091+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 05:05:18 PM UTC 2026
% Result : Theorem 2.15s 1.94s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 145 ( 21 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 188 ( 74 ~; 81 |; 26 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 23 !; 2 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(m__,conjecture,
( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
& aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1021,hypothesis,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1021) ).
fof(m__1098,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1098) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__994) ).
fof(m__1061,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1061) ).
fof(c_0_8,plain,
! [X85,X86,X87,X88,X91,X92,X93,X94,X96,X97] :
( ( aSet0(X87)
| X87 != sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( aElementOf0(esk3_4(X85,X86,X87,X88),X85)
| ~ aElementOf0(X88,X87)
| X87 != sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( aElementOf0(esk4_4(X85,X86,X87,X88),X86)
| ~ aElementOf0(X88,X87)
| X87 != sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( sdtpldt0(esk3_4(X85,X86,X87,X88),esk4_4(X85,X86,X87,X88)) = X88
| ~ aElementOf0(X88,X87)
| X87 != sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( ~ aElementOf0(X92,X85)
| ~ aElementOf0(X93,X86)
| sdtpldt0(X92,X93) != X91
| aElementOf0(X91,X87)
| X87 != sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( ~ aElementOf0(esk5_3(X85,X86,X94),X94)
| ~ aElementOf0(X96,X85)
| ~ aElementOf0(X97,X86)
| sdtpldt0(X96,X97) != esk5_3(X85,X86,X94)
| ~ aSet0(X94)
| X94 = sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( aElementOf0(esk6_3(X85,X86,X94),X85)
| aElementOf0(esk5_3(X85,X86,X94),X94)
| ~ aSet0(X94)
| X94 = sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( aElementOf0(esk7_3(X85,X86,X94),X86)
| aElementOf0(esk5_3(X85,X86,X94),X94)
| ~ aSet0(X94)
| X94 = sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) )
& ( sdtpldt0(esk6_3(X85,X86,X94),esk7_3(X85,X86,X94)) = esk5_3(X85,X86,X94)
| aElementOf0(esk5_3(X85,X86,X94),X94)
| ~ aSet0(X94)
| X94 = sdtpldt1(X85,X86)
| ~ aSet0(X85)
| ~ aSet0(X86) ) ),
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_9,plain,
! [X107,X108,X109,X110,X111] :
( ( aSet0(X107)
| ~ aIdeal0(X107) )
& ( ~ aElementOf0(X109,X107)
| aElementOf0(sdtpldt0(X108,X109),X107)
| ~ aElementOf0(X108,X107)
| ~ aIdeal0(X107) )
& ( ~ aElement0(X110)
| aElementOf0(sdtasdt0(X110,X108),X107)
| ~ aElementOf0(X108,X107)
| ~ aIdeal0(X107) )
& ( aElementOf0(esk9_1(X111),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( aElement0(esk11_1(X111))
| aElementOf0(esk10_1(X111),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X111),esk9_1(X111)),X111)
| aElementOf0(esk10_1(X111),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( aElement0(esk11_1(X111))
| ~ aElementOf0(sdtpldt0(esk9_1(X111),esk10_1(X111)),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X111),esk9_1(X111)),X111)
| ~ aElementOf0(sdtpldt0(esk9_1(X111),esk10_1(X111)),X111)
| ~ aSet0(X111)
| aIdeal0(X111) ) ),
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])])])])])]) ).
cnf(c_0_10,plain,
( aElementOf0(X5,X6)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X4)
| sdtpldt0(X1,X3) != X5
| X6 != sdtpldt1(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_13,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
& aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,plain,
( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(X3,X4))
| ~ aElementOf0(X2,X4)
| ~ aElementOf0(X1,X3)
| ~ aSet0(X4)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_15,hypothesis,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(split_conjunct,[status(thm)],[m__1021]) ).
cnf(c_0_16,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_18,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
inference(fof_nnf,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
( aElementOf0(sdtpldt0(X1,sdtasdt0(xz,xl)),sdtpldt1(X2,xJ))
| ~ aElementOf0(X1,X2)
| ~ aSet0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,hypothesis,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(split_conjunct,[status(thm)],[m__1021]) ).
cnf(c_0_21,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(split_conjunct,[status(thm)],[m__1098]) ).
cnf(c_0_22,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_23,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_26,hypothesis,
( aElementOf0(sdtpldt0(X1,sdtpldt0(xl,xn)),sdtpldt1(X2,xJ))
| ~ aElementOf0(X1,X2)
| ~ aSet0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_16])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_28,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[m__1061]) ).
cnf(c_0_29,negated_conjecture,
~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_22])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG091+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n015.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 01:50:02 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 2.15/1.94 % Version : CSE_E---1.7
% 2.15/1.94 % Problem : theBenchmark.p
% 2.15/1.94 % SZS status Theorem for theBenchmark.p
% 2.15/1.94 % SZS output start CNFRefutation
% See solution above
% 2.15/1.95 % Total time : 1.371s
%------------------------------------------------------------------------------