%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC357+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 : 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 05:19:19 PM UTC 2026
% Result : Theorem 1.44s 1.78s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 144 ( 32 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 175 ( 68 ~; 68 |; 21 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ frontsegP(X4,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ frontsegP(X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_8,plain,
! [X235,X236,X239,X240] :
( ( ssList(esk8_2(X235,X236))
| ~ segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ssList(esk9_2(X235,X236))
| ~ segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( app(app(esk8_2(X235,X236),X236),esk9_2(X235,X236)) = X235
| ~ segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ~ ssList(X239)
| ~ ssList(X240)
| app(app(X239,X236),X240) != X235
| segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
fof(c_0_9,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ~ segmentP(esk49_0,esk48_0)
& ( neq(esk50_0,nil)
| nil = esk51_0 )
& ( frontsegP(esk51_0,esk50_0)
| nil = esk51_0 )
& ( neq(esk50_0,nil)
| nil = esk50_0 )
& ( frontsegP(esk51_0,esk50_0)
| nil = esk50_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_10,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_8]) ).
fof(c_0_11,plain,
! [X342] :
( ~ ssList(X342)
| app(nil,X342) = X342 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_12,plain,
! [X337,X338] :
( ~ ssList(X337)
| ~ ssList(X338)
| ssList(app(X337,X338)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_13,plain,
! [X227,X228,X230] :
( ( ssList(esk6_2(X227,X228))
| ~ frontsegP(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) )
& ( app(X228,esk6_2(X227,X228)) = X227
| ~ frontsegP(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) )
& ( ~ ssList(X230)
| app(X228,X230) != X227
| frontsegP(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,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_10]) ).
cnf(c_0_19,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_21,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
( frontsegP(esk51_0,esk50_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
~ segmentP(esk49_0,esk48_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( app(esk50_0,esk6_2(esk51_0,esk50_0)) = esk51_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
~ segmentP(esk51_0,esk50_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15]),c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( esk50_0 = nil
| ssList(esk6_2(esk51_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_25]),c_0_24])]) ).
cnf(c_0_32,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25])]),c_0_30]),c_0_31]) ).
fof(c_0_33,plain,
! [X401] :
( ~ ssList(X401)
| segmentP(X401,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_34,negated_conjecture,
~ segmentP(esk51_0,nil),
inference(rw,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_35,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC357+1 : TPTP v9.2.1. Released v2.4.0.
% 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
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 04:45:17 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.44/1.78 % Version : CSE_E---1.7
% 1.44/1.78 % Problem : theBenchmark.p
% 1.44/1.78 % SZS status Theorem for theBenchmark.p
% 1.44/1.78 % SZS output start CNFRefutation
% See solution above
% 1.44/1.78 % Total time : 1.369s
%------------------------------------------------------------------------------