%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM020+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 : n001.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 04:13:09 PM UTC 2026
% Result : Theorem 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 17 unt; 0 def)
% Number of atoms : 257 ( 0 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 354 ( 149 ~; 148 |; 43 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 42 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xb,xR,X1)
& sdtmndtasgtdt0(xd,xR,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',mNFRDef) ).
fof(m__715,hypothesis,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3)
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X1,xR,X3) )
=> ( iLess0(X1,xa)
=> ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,xR,X4)
& sdtmndtasgtdt0(X3,xR,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).
fof(m__818,hypothesis,
aNormalFormOfIn0(xd,xw,xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(m__799,hypothesis,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(mReduct,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aReductOfIn0(X3,X1,X2)
=> aElement0(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
fof(mTermin,axiom,
! [X1] :
( aRewritingSystem0(X1)
=> ( isTerminating0(X1)
<=> ! [X2,X3] :
( ( aElement0(X2)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(X2,X1,X3)
=> iLess0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermin) ).
fof(m__731,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(m__755,hypothesis,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
fof(m__656_01,hypothesis,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(mTCRTrans,axiom,
! [X1,X2,X3,X4] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3)
& aElement0(X4) )
=> ( ( sdtmndtasgtdt0(X1,X2,X3)
& sdtmndtasgtdt0(X3,X2,X4) )
=> sdtmndtasgtdt0(X1,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).
fof(c_0_13,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xb,xR,X1)
& sdtmndtasgtdt0(xd,xR,X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_14,plain,
! [X98,X99,X100,X101,X102] :
( ( aElement0(X100)
| ~ aNormalFormOfIn0(X100,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) )
& ( sdtmndtasgtdt0(X98,X99,X100)
| ~ aNormalFormOfIn0(X100,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) )
& ( ~ aReductOfIn0(X101,X100,X99)
| ~ aNormalFormOfIn0(X100,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) )
& ( ~ aElement0(X102)
| ~ sdtmndtasgtdt0(X98,X99,X102)
| aReductOfIn0(esk12_3(X98,X99,X102),X102,X99)
| aNormalFormOfIn0(X102,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) ) ),
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_15,negated_conjecture,
! [X111] :
( ~ aElement0(X111)
| ~ sdtmndtasgtdt0(xb,xR,X111)
| ~ sdtmndtasgtdt0(xd,xR,X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
fof(c_0_16,hypothesis,
! [X107,X108,X109] :
( ( aElement0(esk14_3(X107,X108,X109))
| ~ iLess0(X107,xa)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ aElement0(X109)
| ~ sdtmndtasgtdt0(X107,xR,X108)
| ~ sdtmndtasgtdt0(X107,xR,X109) )
& ( sdtmndtasgtdt0(X108,xR,esk14_3(X107,X108,X109))
| ~ iLess0(X107,xa)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ aElement0(X109)
| ~ sdtmndtasgtdt0(X107,xR,X108)
| ~ sdtmndtasgtdt0(X107,xR,X109) )
& ( sdtmndtasgtdt0(X109,xR,esk14_3(X107,X108,X109))
| ~ iLess0(X107,xa)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ aElement0(X109)
| ~ sdtmndtasgtdt0(X107,xR,X108)
| ~ sdtmndtasgtdt0(X107,xR,X109) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__715])])])]) ).
cnf(c_0_17,plain,
( aElement0(X1)
| ~ aNormalFormOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,hypothesis,
aNormalFormOfIn0(xd,xw,xR),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_19,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]) ).
cnf(c_0_20,hypothesis,
aElement0(xw),
inference(split_conjunct,[status(thm)],[m__799]) ).
fof(c_0_21,plain,
! [X59,X60,X61,X63] :
( ( aElement0(esk1_3(X59,X60,X61))
| aReductOfIn0(X61,X59,X60)
| ~ sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( aReductOfIn0(esk1_3(X59,X60,X61),X59,X60)
| aReductOfIn0(X61,X59,X60)
| ~ sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( sdtmndtplgtdt0(esk1_3(X59,X60,X61),X60,X61)
| aReductOfIn0(X61,X59,X60)
| ~ sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( ~ aReductOfIn0(X61,X59,X60)
| sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( ~ aElement0(X63)
| ~ aReductOfIn0(X63,X59,X60)
| ~ sdtmndtplgtdt0(X63,X60,X61)
| sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCDef])])])])]) ).
fof(c_0_22,plain,
! [X56,X57,X58] :
( ~ aElement0(X56)
| ~ aRewritingSystem0(X57)
| ~ aReductOfIn0(X58,X56,X57)
| aElement0(X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mReduct])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ aElement0(X1)
| ~ sdtmndtasgtdt0(xb,xR,X1)
| ~ sdtmndtasgtdt0(xd,xR,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X3,X1))
| ~ iLess0(X2,xa)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X2,xR,X3)
| ~ sdtmndtasgtdt0(X2,xR,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,hypothesis,
aElement0(xd),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
fof(c_0_26,plain,
! [X93,X94,X95] :
( ( ~ isTerminating0(X93)
| ~ aElement0(X94)
| ~ aElement0(X95)
| ~ sdtmndtplgtdt0(X94,X93,X95)
| iLess0(X95,X94)
| ~ aRewritingSystem0(X93) )
& ( aElement0(esk10_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) )
& ( aElement0(esk11_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) )
& ( sdtmndtplgtdt0(esk10_1(X93),X93,esk11_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) )
& ( ~ iLess0(esk11_1(X93),esk10_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTermin])])])])]) ).
cnf(c_0_27,plain,
( sdtmndtplgtdt0(X2,X3,X1)
| ~ aReductOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( aElement0(X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aReductOfIn0(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( ~ sdtmndtasgtdt0(xb,xR,esk14_3(X1,X2,xd))
| ~ sdtmndtasgtdt0(X1,xR,xd)
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ iLess0(X1,xa)
| ~ aElement0(esk14_3(X1,X2,xd))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,hypothesis,
( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X1,X3))
| ~ iLess0(X2,xa)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X2,xR,X1)
| ~ sdtmndtasgtdt0(X2,xR,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__731]) ).
cnf(c_0_32,plain,
( iLess0(X3,X2)
| ~ isTerminating0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( sdtmndtplgtdt0(X1,X2,X3)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( ~ sdtmndtasgtdt0(X1,xR,xd)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ iLess0(X1,xa)
| ~ aElement0(esk14_3(X1,xb,xd))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_25])]) ).
cnf(c_0_35,hypothesis,
( aElement0(esk14_3(X1,X2,X3))
| ~ iLess0(X1,xa)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ sdtmndtasgtdt0(X1,xR,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_36,plain,
( iLess0(X1,X2)
| ~ isTerminating0(X3)
| ~ aReductOfIn0(X1,X2,X3)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]) ).
cnf(c_0_37,hypothesis,
aReductOfIn0(xu,xa,xR),
inference(split_conjunct,[status(thm)],[m__755]) ).
cnf(c_0_38,hypothesis,
isTerminating0(xR),
inference(split_conjunct,[status(thm)],[m__656_01]) ).
cnf(c_0_39,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__731]) ).
fof(c_0_40,plain,
! [X71,X72,X73,X74] :
( ~ aElement0(X71)
| ~ aRewritingSystem0(X72)
| ~ aElement0(X73)
| ~ aElement0(X74)
| ~ sdtmndtasgtdt0(X71,X72,X73)
| ~ sdtmndtasgtdt0(X73,X72,X74)
| sdtmndtasgtdt0(X71,X72,X74) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCRTrans])]) ).
cnf(c_0_41,plain,
( sdtmndtasgtdt0(X1,X2,X3)
| ~ aNormalFormOfIn0(X3,X1,X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,hypothesis,
( ~ sdtmndtasgtdt0(X1,xR,xd)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ iLess0(X1,xa)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_25]),c_0_31])]) ).
cnf(c_0_43,hypothesis,
iLess0(xu,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_19]),c_0_39])]) ).
cnf(c_0_44,hypothesis,
sdtmndtasgtdt0(xu,xR,xb),
inference(split_conjunct,[status(thm)],[m__755]) ).
cnf(c_0_45,hypothesis,
aElement0(xu),
inference(split_conjunct,[status(thm)],[m__755]) ).
cnf(c_0_46,plain,
( sdtmndtasgtdt0(X1,X2,X4)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtmndtasgtdt0(X1,X2,X3)
| ~ sdtmndtasgtdt0(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,hypothesis,
sdtmndtasgtdt0(xw,xR,xd),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_48,hypothesis,
~ sdtmndtasgtdt0(xu,xR,xd),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
cnf(c_0_49,hypothesis,
( sdtmndtasgtdt0(X1,xR,xd)
| ~ sdtmndtasgtdt0(X1,xR,xw)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_19]),c_0_25]),c_0_20])]) ).
cnf(c_0_50,hypothesis,
sdtmndtasgtdt0(xu,xR,xw),
inference(split_conjunct,[status(thm)],[m__799]) ).
cnf(c_0_51,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : COM020+1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 16:20:33 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------