%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG090+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 : n011.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 116.64s 57.23s
% Output : CNFRefutation 117.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 22 unt; 0 def)
% Number of atoms : 122 ( 18 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 127 ( 49 ~; 50 |; 19 &)
% ( 1 <=>; 8 =>; 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 : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
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(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
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__967,hypothesis,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& xy = sdtpldt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).
fof(c_0_10,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])])])])])]) ).
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,
! [X61,X62,X63] :
( ~ aElement0(X61)
| ~ aElement0(X62)
| ~ aElement0(X63)
| sdtpldt0(sdtpldt0(X61,X62),X63) = sdtpldt0(X61,sdtpldt0(X62,X63)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_13,plain,
! [X59,X60] :
( ~ aElement0(X59)
| ~ aElement0(X60)
| sdtpldt0(X59,X60) = sdtpldt0(X60,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_14,plain,
! [X79,X80] :
( ~ aSet0(X79)
| ~ aElementOf0(X80,X79)
| aElement0(X80) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_15,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_17,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_18,plain,
! [X55,X56] :
( ~ aElement0(X55)
| ~ aElement0(X56)
| aElement0(sdtpldt0(X55,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_19,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,hypothesis,
xx = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_21,hypothesis,
xy = sdtpldt0(xm,xn),
inference(split_conjunct,[status(thm)],[m__967]) ).
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,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_26,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_28,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xm,xI),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_30,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,negated_conjecture,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_32,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X2,sdtpldt0(X1,X3))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_33,hypothesis,
aElement0(sdtpldt0(xl,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_34,hypothesis,
aElement0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_27]),c_0_28])]) ).
cnf(c_0_35,hypothesis,
aElement0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_29]),c_0_28])]) ).
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_23,c_0_22]),c_0_30]) ).
cnf(c_0_37,hypothesis,
aElementOf0(xn,xJ),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_38,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_39,negated_conjecture,
sdtpldt0(xm,sdtpldt0(xk,sdtpldt0(xl,xn))) != sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[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]),c_0_35])]) ).
cnf(c_0_40,plain,
( sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(X3,X4))) = sdtpldt0(sdtpldt0(X2,X3),sdtpldt0(X1,X4))
| ~ aElement0(X4)
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_36]),c_0_30]) ).
cnf(c_0_41,hypothesis,
aElement0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_37]),c_0_26])]) ).
cnf(c_0_42,hypothesis,
aElement0(xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_38]),c_0_26])]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_35]),c_0_42]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG090+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % 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
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 01:49:32 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 116.64/57.23 % Version : CSE_E---1.7
% 116.64/57.23 % Problem : theBenchmark.p
% 116.64/57.23 % SZS status Theorem for theBenchmark.p
% 116.64/57.23 % SZS output start CNFRefutation
% See solution above
% 117.04/57.64 % Total time : 42.913s
%------------------------------------------------------------------------------