%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC071+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n005.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 05:18:08 PM UTC 2026
% Result : Theorem 1.32s 1.69s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 203 ( 64 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 250 ( 88 ~; 94 |; 45 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 33 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( nil = X2
& nil = X1 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( cons(X6,nil) != X3
| app(app(X7,X3),X8) != X4
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X6,X9) )
| ? [X10] :
( ssItem(X10)
& memberP(X8,X10)
& lt(X10,X6) ) ) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( nil = X2
& nil = X1 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( cons(X6,nil) != X3
| app(app(X7,X3),X8) != X4
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X6,X9) )
| ? [X10] :
( ssItem(X10)
& memberP(X8,X10)
& lt(X10,X6) ) ) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_7,negated_conjecture,
! [X472,X476,X477] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssList(X472)
| ~ neq(X472,nil)
| ~ segmentP(esk49_0,X472)
| ~ segmentP(esk48_0,X472) )
& ( nil != esk49_0
| nil != esk48_0 )
& ( nil = esk51_0
| ssItem(esk52_0) )
& ( nil = esk50_0
| ssItem(esk52_0) )
& ( nil = esk51_0
| ssList(esk53_0) )
& ( nil = esk50_0
| ssList(esk53_0) )
& ( nil = esk51_0
| ssList(esk54_0) )
& ( nil = esk50_0
| ssList(esk54_0) )
& ( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk51_0
| app(app(esk53_0,esk50_0),esk54_0) = esk51_0 )
& ( nil = esk50_0
| app(app(esk53_0,esk50_0),esk54_0) = esk51_0 )
& ( nil = esk51_0
| ~ ssItem(X476)
| ~ memberP(esk53_0,X476)
| ~ lt(esk52_0,X476) )
& ( nil = esk50_0
| ~ ssItem(X476)
| ~ memberP(esk53_0,X476)
| ~ lt(esk52_0,X476) )
& ( nil = esk51_0
| ~ ssItem(X477)
| ~ memberP(esk54_0,X477)
| ~ lt(X477,esk52_0) )
& ( nil = esk50_0
| ~ ssItem(X477)
| ~ memberP(esk54_0,X477)
| ~ lt(X477,esk52_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_8,plain,
! [X330,X331] :
( ~ ssList(X330)
| ~ ssItem(X331)
| cons(X331,X330) != X330 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_9,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X245,X246,X249,X250] :
( ( ssList(esk8_2(X245,X246))
| ~ segmentP(X245,X246)
| ~ ssList(X246)
| ~ ssList(X245) )
& ( ssList(esk9_2(X245,X246))
| ~ segmentP(X245,X246)
| ~ ssList(X246)
| ~ ssList(X245) )
& ( app(app(esk8_2(X245,X246),X246),esk9_2(X245,X246)) = X245
| ~ segmentP(X245,X246)
| ~ ssList(X246)
| ~ ssList(X245) )
& ( ~ ssList(X249)
| ~ ssList(X250)
| app(app(X249,X246),X250) != X245
| segmentP(X245,X246)
| ~ ssList(X246)
| ~ ssList(X245) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
cnf(c_0_13,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_16,negated_conjecture,
( nil = esk51_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( esk50_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_19,plain,
! [X406] :
( ~ ssList(X406)
| segmentP(X406,X406) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( nil = esk50_0
| app(app(esk53_0,esk50_0),esk54_0) = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
esk50_0 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),c_0_16]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( nil = esk50_0
| ssList(esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
( nil = esk50_0
| ssList(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
( ~ segmentP(esk50_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_10]),c_0_11]) ).
cnf(c_0_28,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_30,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
app(app(esk53_0,esk50_0),esk54_0) = esk51_0,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk54_0),
inference(sr,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_34,negated_conjecture,
ssList(esk53_0),
inference(sr,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_36,negated_conjecture,
segmentP(esk51_0,esk50_0),
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_30,c_0_31]),c_0_32]),c_0_29]),c_0_33]),c_0_34])]) ).
fof(c_0_37,plain,
! [X326,X327] :
( ( ~ neq(X326,X327)
| X326 != X327
| ~ ssList(X327)
| ~ ssList(X326) )
& ( X326 = X327
| neq(X326,X327)
| ~ ssList(X327)
| ~ ssList(X326) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_38,negated_conjecture,
~ neq(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_39,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_15]),c_0_29])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC071+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.09 % 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
% 0.10/0.29 % Computer : n005.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue May 5 04:22:45 EDT 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.30 % start to proof: theBenchmark
% 1.32/1.69 % Version : CSE_E---1.7
% 1.32/1.69 % Problem : theBenchmark.p
% 1.32/1.69 % SZS status Theorem for theBenchmark.p
% 1.32/1.69 % SZS output start CNFRefutation
% See solution above
% 1.32/1.69 % Total time : 1.369s
%------------------------------------------------------------------------------