%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG090+2 : 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 : n017.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 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 23 unt; 0 def)
% Number of atoms : 104 ( 19 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 96 ( 34 ~; 28 |; 23 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__870,hypothesis,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X1] :
( aElementOf0(X1,xJ)
=> ( ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X1,X2),xJ) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(m__,conjecture,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(m__967,hypothesis,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& xy = sdtpldt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
fof(m__934,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_9,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])])]) ).
fof(c_0_10,hypothesis,
! [X125,X126,X127,X128,X129,X130] :
( aSet0(xI)
& ( ~ aElementOf0(X126,xI)
| aElementOf0(sdtpldt0(X125,X126),xI)
| ~ aElementOf0(X125,xI) )
& ( ~ aElement0(X127)
| aElementOf0(sdtasdt0(X127,X125),xI)
| ~ aElementOf0(X125,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X129,xJ)
| aElementOf0(sdtpldt0(X128,X129),xJ)
| ~ aElementOf0(X128,xJ) )
& ( ~ aElement0(X130)
| aElementOf0(sdtasdt0(X130,X128),xJ)
| ~ aElementOf0(X128,xJ) )
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__870])])])]) ).
fof(c_0_11,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_12,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])]) ).
cnf(c_0_13,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(xn,xJ),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_15,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xm,xI),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_17,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,hypothesis,
xx = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_20,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_21,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_22,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,hypothesis,
xy = sdtpldt0(xm,xn),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_24,hypothesis,
aElement0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_25,hypothesis,
aElement0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_17])]) ).
fof(c_0_26,plain,
! [X69,X70] :
( ~ aElement0(X69)
| ~ aElement0(X70)
| sdtpldt0(X69,X70) = sdtpldt0(X70,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_27,negated_conjecture,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(sdtpldt0(xk,xl),xy),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,hypothesis,
aElement0(sdtpldt0(xl,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_20]),c_0_15])]) ).
cnf(c_0_29,hypothesis,
aElement0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_17])]) ).
cnf(c_0_30,hypothesis,
( sdtpldt0(xm,sdtpldt0(xn,X1)) = sdtpldt0(xy,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
fof(c_0_33,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_34,negated_conjecture,
sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(sdtpldt0(xk,xl),xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_28]),c_0_25]),c_0_29])]) ).
cnf(c_0_35,hypothesis,
( sdtpldt0(xm,sdtpldt0(X1,xn)) = sdtpldt0(xy,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24])]) ).
cnf(c_0_36,hypothesis,
aElement0(xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_32]),c_0_15])]) ).
cnf(c_0_37,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
sdtpldt0(xk,sdtpldt0(xy,xl)) != sdtpldt0(sdtpldt0(xk,xl),xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,hypothesis,
aElement0(xy),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_40,negated_conjecture,
sdtpldt0(sdtpldt0(xk,xl),xy) != sdtpldt0(xk,sdtpldt0(xl,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_36]),c_0_39])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_22]),c_0_39]),c_0_36]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG090+2 : 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
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:48:43 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------