%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC399+1 : TPTP v9.2.1. Released v2.4.0.
% 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 05:19:30 PM UTC 2026
% Result : Theorem 1.78s 1.88s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 20 unt; 0 def)
% Number of atoms : 202 ( 47 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 255 ( 98 ~; 98 |; 38 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 41 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,X3),X6) != X4
| ~ equalelemsP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssList(X9)
& app(cons(X7,nil),X9) = X3 ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X6
& ? [X12] :
( ssList(X12)
& app(X12,cons(X10,nil)) = X3 ) ) ) ) )
| ! [X13] :
( ~ ssItem(X13)
| ~ memberP(X1,X13)
| memberP(X2,X13) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(c_0_5,plain,
! [X247,X248,X250] :
( ( ssList(esk7_2(X247,X248))
| ~ rearsegP(X247,X248)
| ~ ssList(X248)
| ~ ssList(X247) )
& ( app(esk7_2(X247,X248),X248) = X247
| ~ rearsegP(X247,X248)
| ~ ssList(X248)
| ~ ssList(X247) )
& ( ~ ssList(X250)
| app(X250,X248) != X247
| rearsegP(X247,X248)
| ~ ssList(X248)
| ~ ssList(X247) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
fof(c_0_6,plain,
! [X353,X354] :
( ~ ssList(X353)
| ~ ssList(X354)
| ssList(app(X353,X354)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,X3),X6) != X4
| ~ equalelemsP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssList(X9)
& app(cons(X7,nil),X9) = X3 ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X6
& ? [X12] :
( ssList(X12)
& app(X12,cons(X10,nil)) = X3 ) ) ) ) )
| ! [X13] :
( ~ ssItem(X13)
| ~ memberP(X1,X13)
| memberP(X2,X13) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_8,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
! [X480,X481,X482,X483,X484,X485] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& ssList(esk53_0)
& app(app(esk52_0,esk50_0),esk53_0) = esk51_0
& equalelemsP(esk50_0)
& ( ~ ssItem(X480)
| ~ ssList(X481)
| app(X481,cons(X480,nil)) != esk52_0
| ~ ssList(X482)
| app(cons(X480,nil),X482) != esk50_0 )
& ( ~ ssItem(X483)
| ~ ssList(X484)
| app(cons(X483,nil),X484) != esk53_0
| ~ ssList(X485)
| app(X485,cons(X483,nil)) != esk50_0 )
& ssItem(esk54_0)
& memberP(esk48_0,esk54_0)
& ~ memberP(esk49_0,esk54_0)
& ( nil = esk51_0
| nil != esk50_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X437,X438,X439] :
( ~ ssList(X437)
| ~ ssList(X438)
| ~ ssList(X439)
| app(X439,X438) != app(X437,X438)
| X439 = X437 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
cnf(c_0_12,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_8]),c_0_9]) ).
cnf(c_0_13,negated_conjecture,
app(app(esk52_0,esk50_0),esk53_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( rearsegP(esk51_0,esk53_0)
| ~ ssList(app(esk52_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_23,plain,
! [X374,X375,X376] :
( ( ~ memberP(app(X375,X376),X374)
| memberP(X375,X374)
| memberP(X376,X374)
| ~ ssList(X376)
| ~ ssList(X375)
| ~ ssItem(X374) )
& ( ~ memberP(X375,X374)
| memberP(app(X375,X376),X374)
| ~ ssList(X376)
| ~ ssList(X375)
| ~ ssItem(X374) )
& ( ~ memberP(X376,X374)
| memberP(app(X375,X376),X374)
| ~ ssList(X376)
| ~ ssList(X375)
| ~ ssItem(X374) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_24,negated_conjecture,
memberP(esk48_0,esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( X1 = app(esk52_0,esk50_0)
| app(X1,esk53_0) != esk51_0
| ~ ssList(app(esk52_0,esk50_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_14])]) ).
cnf(c_0_26,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_27,negated_conjecture,
rearsegP(esk51_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_9]),c_0_19]),c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_30,plain,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
memberP(esk50_0,esk54_0),
inference(rw,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_32,negated_conjecture,
ssItem(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,negated_conjecture,
( X1 = app(esk52_0,esk50_0)
| app(X1,esk53_0) != esk51_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_9]),c_0_19]),c_0_20])]) ).
cnf(c_0_34,negated_conjecture,
app(esk7_2(esk51_0,esk53_0),esk53_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14]),c_0_28])]) ).
cnf(c_0_35,negated_conjecture,
ssList(esk7_2(esk51_0,esk53_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_14]),c_0_28])]) ).
cnf(c_0_36,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_37,negated_conjecture,
( memberP(app(X1,esk50_0),esk54_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19]),c_0_32])]) ).
cnf(c_0_38,negated_conjecture,
esk7_2(esk51_0,esk53_0) = app(esk52_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_39,negated_conjecture,
( memberP(app(app(X1,esk50_0),X2),esk54_0)
| ~ ssList(app(X1,esk50_0))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_32])]) ).
cnf(c_0_40,negated_conjecture,
ssList(app(esk52_0,esk50_0)),
inference(rw,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
~ memberP(esk49_0,esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_42,negated_conjecture,
( memberP(app(app(esk52_0,esk50_0),X1),esk54_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20])]) ).
cnf(c_0_43,negated_conjecture,
~ memberP(esk51_0,esk54_0),
inference(rw,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_13]),c_0_14])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC399+1 : TPTP v9.2.1. Released v2.4.0.
% 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
% 0.16/0.32 % Computer : n002.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 04:48:16 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.78/1.88 % Version : CSE_E---1.7
% 1.78/1.88 % Problem : theBenchmark.p
% 1.78/1.88 % SZS status Theorem for theBenchmark.p
% 1.78/1.88 % SZS output start CNFRefutation
% See solution above
% 1.78/1.88 % Total time : 1.372s
%------------------------------------------------------------------------------