%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG095+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 : n002.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 05:05:19 PM UTC 2026
% Result : Theorem 20.63s 12.80s
% Output : CNFRefutation 20.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 16 unt; 0 def)
% Number of atoms : 233 ( 43 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 306 ( 129 ~; 131 |; 32 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 100 ( 0 sgn 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(m__1205_03,hypothesis,
! [X1] :
( aElement0(X1)
=> aElementOf0(X1,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205_03) ).
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(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__1205,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_12,negated_conjecture,
~ ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = sz10 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_13,plain,
! [X95,X96,X97,X98,X101,X102,X103,X104,X106,X107] :
( ( aSet0(X97)
| X97 != sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( aElementOf0(esk3_4(X95,X96,X97,X98),X95)
| ~ aElementOf0(X98,X97)
| X97 != sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( aElementOf0(esk4_4(X95,X96,X97,X98),X96)
| ~ aElementOf0(X98,X97)
| X97 != sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( sdtpldt0(esk3_4(X95,X96,X97,X98),esk4_4(X95,X96,X97,X98)) = X98
| ~ aElementOf0(X98,X97)
| X97 != sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( ~ aElementOf0(X102,X95)
| ~ aElementOf0(X103,X96)
| sdtpldt0(X102,X103) != X101
| aElementOf0(X101,X97)
| X97 != sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( ~ aElementOf0(esk5_3(X95,X96,X104),X104)
| ~ aElementOf0(X106,X95)
| ~ aElementOf0(X107,X96)
| sdtpldt0(X106,X107) != esk5_3(X95,X96,X104)
| ~ aSet0(X104)
| X104 = sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( aElementOf0(esk6_3(X95,X96,X104),X95)
| aElementOf0(esk5_3(X95,X96,X104),X104)
| ~ aSet0(X104)
| X104 = sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( aElementOf0(esk7_3(X95,X96,X104),X96)
| aElementOf0(esk5_3(X95,X96,X104),X104)
| ~ aSet0(X104)
| X104 = sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) )
& ( sdtpldt0(esk6_3(X95,X96,X104),esk7_3(X95,X96,X104)) = esk5_3(X95,X96,X104)
| aElementOf0(esk5_3(X95,X96,X104),X104)
| ~ aSet0(X104)
| X104 = sdtpldt1(X95,X96)
| ~ aSet0(X95)
| ~ aSet0(X96) ) ),
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_14,hypothesis,
! [X132] :
( ~ aElement0(X132)
| aElementOf0(X132,sdtpldt1(xI,xJ)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205_03])]) ).
fof(c_0_15,plain,
! [X117,X118,X119,X120,X121] :
( ( aSet0(X117)
| ~ aIdeal0(X117) )
& ( ~ aElementOf0(X119,X117)
| aElementOf0(sdtpldt0(X118,X119),X117)
| ~ aElementOf0(X118,X117)
| ~ aIdeal0(X117) )
& ( ~ aElement0(X120)
| aElementOf0(sdtasdt0(X120,X118),X117)
| ~ aElementOf0(X118,X117)
| ~ aIdeal0(X117) )
& ( aElementOf0(esk9_1(X121),X121)
| ~ aSet0(X121)
| aIdeal0(X121) )
& ( aElement0(esk11_1(X121))
| aElementOf0(esk10_1(X121),X121)
| ~ aSet0(X121)
| aIdeal0(X121) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X121),esk9_1(X121)),X121)
| aElementOf0(esk10_1(X121),X121)
| ~ aSet0(X121)
| aIdeal0(X121) )
& ( aElement0(esk11_1(X121))
| ~ aElementOf0(sdtpldt0(esk9_1(X121),esk10_1(X121)),X121)
| ~ aSet0(X121)
| aIdeal0(X121) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X121),esk9_1(X121)),X121)
| ~ aElementOf0(sdtpldt0(esk9_1(X121),esk10_1(X121)),X121)
| ~ aSet0(X121)
| aIdeal0(X121) ) ),
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_16,negated_conjecture,
! [X133,X134] :
( ~ aElementOf0(X133,xI)
| ~ aElementOf0(X134,xJ)
| sdtpldt0(X133,X134) != sz10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_17,plain,
! [X69,X70] :
( ~ aElement0(X69)
| ~ aElement0(X70)
| sdtpldt0(X69,X70) = sdtpldt0(X70,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_18,plain,
! [X71,X72,X73] :
( ~ aElement0(X71)
| ~ aElement0(X72)
| ~ aElement0(X73)
| sdtpldt0(sdtpldt0(X71,X72),X73) = sdtpldt0(X71,sdtpldt0(X72,X73)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_19,plain,
! [X65,X66] :
( ~ aElement0(X65)
| ~ aElement0(X66)
| aElement0(sdtpldt0(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_20,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_13]) ).
cnf(c_0_21,hypothesis,
( aElementOf0(X1,sdtpldt1(xI,xJ))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_23,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__1205]) ).
cnf(c_0_25,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__1205]) ).
cnf(c_0_26,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xJ)
| sdtpldt0(X1,X2) != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_30,plain,
! [X89,X90] :
( ~ aSet0(X89)
| ~ aElementOf0(X90,X89)
| aElement0(X90) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_31,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_20]) ).
cnf(c_0_32,hypothesis,
aElementOf0(sz10,sdtpldt1(xI,xJ)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_33,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_34,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_35,negated_conjecture,
( sdtpldt0(X1,X2) != sz10
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X2,xI)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_37,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,hypothesis,
aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz10),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_39,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_13]) ).
cnf(c_0_40,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(X2,X3)) != sz10
| ~ aElementOf0(sdtpldt0(X3,X1),xI)
| ~ aElementOf0(X2,xJ)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_29]) ).
cnf(c_0_41,hypothesis,
aElement0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]) ).
fof(c_0_42,plain,
! [X74] :
( ( sdtpldt0(X74,sz00) = X74
| ~ aElement0(X74) )
& ( X74 = sdtpldt0(sz00,X74)
| ~ aElement0(X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_43,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_39]) ).
cnf(c_0_44,hypothesis,
( sdtpldt0(X1,sdtpldt0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz10),X2)) != sz10
| ~ aElementOf0(sdtpldt0(X2,X1),xI)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_41])]) ).
cnf(c_0_45,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_47,hypothesis,
aElementOf0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),sz10),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_48,hypothesis,
( sdtpldt0(X1,sdtpldt0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz10),sz00)) != sz10
| ~ aElementOf0(X1,xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_49,hypothesis,
aElement0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_47]),c_0_34])]) ).
cnf(c_0_50,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_13]) ).
cnf(c_0_51,hypothesis,
sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),sz10),sdtpldt0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz10),sz00)) != sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_49])]) ).
cnf(c_0_52,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,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_50]) ).
cnf(c_0_54,hypothesis,
sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),sz10),esk4_4(xI,xJ,sdtpldt1(xI,xJ),sz10)) != sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_41])]) ).
cnf(c_0_55,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_32]),c_0_33]),c_0_34])]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG095+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n002.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:50:01 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 20.63/12.80 % Version : CSE_E---1.7
% 20.63/12.80 % Problem : theBenchmark.p
% 20.63/12.80 % SZS status Theorem for theBenchmark.p
% 20.63/12.80 % SZS output start CNFRefutation
% See solution above
% 20.63/12.88 % Total time : 9.383s
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