%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM021+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 : n008.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 04:13:10 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 127 ( 6 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 166 ( 67 ~; 71 |; 22 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 37 ( 2 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mNFRDef,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aNormalFormOfIn0(X3,X1,X2)
<=> ( aElement0(X3)
& sdtmndtasgtdt0(X1,X2,X3)
& ~ ? [X4] : aReductOfIn0(X4,X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
fof(mTCRDef,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3) )
=> ( sdtmndtasgtdt0(X1,X2,X3)
<=> ( X1 = X3
| sdtmndtplgtdt0(X1,X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
fof(m__818,hypothesis,
aNormalFormOfIn0(xd,xw,xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(m__799,hypothesis,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
fof(mTCDef,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(X1,X2,X3)
<=> ( aReductOfIn0(X3,X1,X2)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,X2)
& sdtmndtplgtdt0(X4,X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCDef) ).
fof(m__850,hypothesis,
( aElement0(xx)
& sdtmndtasgtdt0(xb,xR,xx)
& sdtmndtasgtdt0(xd,xR,xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__850) ).
fof(m__,conjecture,
sdtmndtasgtdt0(xb,xR,xd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_8,plain,
! [X97,X98,X99,X100,X101] :
( ( aElement0(X99)
| ~ aNormalFormOfIn0(X99,X97,X98)
| ~ aElement0(X97)
| ~ aRewritingSystem0(X98) )
& ( sdtmndtasgtdt0(X97,X98,X99)
| ~ aNormalFormOfIn0(X99,X97,X98)
| ~ aElement0(X97)
| ~ aRewritingSystem0(X98) )
& ( ~ aReductOfIn0(X100,X99,X98)
| ~ aNormalFormOfIn0(X99,X97,X98)
| ~ aElement0(X97)
| ~ aRewritingSystem0(X98) )
& ( ~ aElement0(X101)
| ~ sdtmndtasgtdt0(X97,X98,X101)
| aReductOfIn0(esk12_3(X97,X98,X101),X101,X98)
| aNormalFormOfIn0(X101,X97,X98)
| ~ aElement0(X97)
| ~ aRewritingSystem0(X98) ) ),
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)],[mNFRDef])])])])])]) ).
fof(c_0_9,plain,
! [X67,X68,X69] :
( ( ~ sdtmndtasgtdt0(X67,X68,X69)
| X67 = X69
| sdtmndtplgtdt0(X67,X68,X69)
| ~ aElement0(X67)
| ~ aRewritingSystem0(X68)
| ~ aElement0(X69) )
& ( X67 != X69
| sdtmndtasgtdt0(X67,X68,X69)
| ~ aElement0(X67)
| ~ aRewritingSystem0(X68)
| ~ aElement0(X69) )
& ( ~ sdtmndtplgtdt0(X67,X68,X69)
| sdtmndtasgtdt0(X67,X68,X69)
| ~ aElement0(X67)
| ~ aRewritingSystem0(X68)
| ~ aElement0(X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCRDef])])]) ).
cnf(c_0_10,plain,
( aElement0(X1)
| ~ aNormalFormOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
aNormalFormOfIn0(xd,xw,xR),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_12,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]) ).
cnf(c_0_13,hypothesis,
aElement0(xw),
inference(split_conjunct,[status(thm)],[m__799]) ).
fof(c_0_14,plain,
! [X58,X59,X60,X62] :
( ( aElement0(esk1_3(X58,X59,X60))
| aReductOfIn0(X60,X58,X59)
| ~ sdtmndtplgtdt0(X58,X59,X60)
| ~ aElement0(X58)
| ~ aRewritingSystem0(X59)
| ~ aElement0(X60) )
& ( aReductOfIn0(esk1_3(X58,X59,X60),X58,X59)
| aReductOfIn0(X60,X58,X59)
| ~ sdtmndtplgtdt0(X58,X59,X60)
| ~ aElement0(X58)
| ~ aRewritingSystem0(X59)
| ~ aElement0(X60) )
& ( sdtmndtplgtdt0(esk1_3(X58,X59,X60),X59,X60)
| aReductOfIn0(X60,X58,X59)
| ~ sdtmndtplgtdt0(X58,X59,X60)
| ~ aElement0(X58)
| ~ aRewritingSystem0(X59)
| ~ aElement0(X60) )
& ( ~ aReductOfIn0(X60,X58,X59)
| sdtmndtplgtdt0(X58,X59,X60)
| ~ aElement0(X58)
| ~ aRewritingSystem0(X59)
| ~ aElement0(X60) )
& ( ~ aElement0(X62)
| ~ aReductOfIn0(X62,X58,X59)
| ~ sdtmndtplgtdt0(X62,X59,X60)
| sdtmndtplgtdt0(X58,X59,X60)
| ~ aElement0(X58)
| ~ aRewritingSystem0(X59)
| ~ aElement0(X60) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCDef])])])])]) ).
cnf(c_0_15,plain,
( X1 = X3
| sdtmndtplgtdt0(X1,X2,X3)
| ~ sdtmndtasgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,hypothesis,
sdtmndtasgtdt0(xd,xR,xx),
inference(split_conjunct,[status(thm)],[m__850]) ).
cnf(c_0_17,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__850]) ).
cnf(c_0_18,hypothesis,
aElement0(xd),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_19,plain,
( ~ aReductOfIn0(X1,X2,X3)
| ~ aNormalFormOfIn0(X2,X4,X3)
| ~ aElement0(X4)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_20,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_21,plain,
( aReductOfIn0(esk1_3(X1,X2,X3),X1,X2)
| aReductOfIn0(X3,X1,X2)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
( xd = xx
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]),c_0_17]),c_0_18])]) ).
cnf(c_0_23,hypothesis,
~ aReductOfIn0(X1,xd,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_24,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,hypothesis,
xd = xx,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_12]),c_0_17]),c_0_18])]),c_0_23]),c_0_23]) ).
cnf(c_0_26,hypothesis,
sdtmndtasgtdt0(xb,xR,xx),
inference(split_conjunct,[status(thm)],[m__850]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM021+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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 : n008.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 : Mon May 4 16:19:58 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------