%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC305+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 : n018.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 05:19:06 PM UTC 2026
% Result : Theorem 1.59s 1.80s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 20 unt; 0 def)
% Number of atoms : 200 ( 30 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 236 ( 83 ~; 82 |; 30 &)
% ( 1 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& strictorderedP(X5) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) != X1
| ~ lt(X7,X6) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax33,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax33) ).
fof(ax12,axiom,
! [X1] :
( ssList(X1)
=> ( strictorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> lt(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& strictorderedP(X5) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) != X1
| ~ lt(X7,X6) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_9,negated_conjecture,
! [X472] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& frontsegP(esk51_0,esk50_0)
& strictorderedP(esk50_0)
& ( ~ ssList(X472)
| ~ neq(esk50_0,X472)
| ~ frontsegP(esk51_0,X472)
| ~ segmentP(X472,esk50_0)
| ~ strictorderedP(X472) )
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& ssList(esk56_0)
& app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
& lt(esk53_0,esk52_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_10,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_11,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X439,X440,X441] :
( ~ ssList(X439)
| ~ ssList(X440)
| ~ ssList(X441)
| app(app(X439,X440),X441) = app(X439,app(X440,X441)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_13,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_17,plain,
! [X328,X329] :
( ~ ssList(X328)
| ~ ssItem(X329)
| ssList(cons(X329,X328)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_18,negated_conjecture,
( app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_19,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_21,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,plain,
! [X437,X438] :
( ~ ssList(X437)
| ~ ssItem(X438)
| cons(X438,X437) = app(cons(X438,nil),X437) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_23,negated_conjecture,
app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[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_24,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]),c_0_21])]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_25]),c_0_26])]) ).
cnf(c_0_28,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_29,plain,
! [X347,X348] :
( ~ ssList(X347)
| ~ ssList(X348)
| ssList(app(X347,X348)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_30,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_20]),c_0_28])]) ).
cnf(c_0_31,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_32,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax33]) ).
fof(c_0_33,plain,
! [X295,X296,X297,X298,X299,X300] :
( ( ~ strictorderedP(X295)
| ~ ssItem(X296)
| ~ ssItem(X297)
| ~ ssList(X298)
| ~ ssList(X299)
| ~ ssList(X300)
| app(app(X298,cons(X296,X299)),cons(X297,X300)) != X295
| lt(X296,X297)
| ~ ssList(X295) )
& ( ssItem(esk30_1(X295))
| strictorderedP(X295)
| ~ ssList(X295) )
& ( ssItem(esk31_1(X295))
| strictorderedP(X295)
| ~ ssList(X295) )
& ( ssList(esk32_1(X295))
| strictorderedP(X295)
| ~ ssList(X295) )
& ( ssList(esk33_1(X295))
| strictorderedP(X295)
| ~ ssList(X295) )
& ( ssList(esk34_1(X295))
| strictorderedP(X295)
| ~ ssList(X295) )
& ( app(app(esk32_1(X295),cons(esk30_1(X295),esk33_1(X295))),cons(esk31_1(X295),esk34_1(X295))) = X295
| strictorderedP(X295)
| ~ ssList(X295) )
& ( ~ lt(esk30_1(X295),esk31_1(X295))
| strictorderedP(X295)
| ~ ssList(X295) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])]) ).
cnf(c_0_34,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_16])]) ).
fof(c_0_35,plain,
! [X361,X362] :
( ~ ssItem(X361)
| ~ ssItem(X362)
| ~ lt(X361,X362)
| ~ lt(X362,X361) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
cnf(c_0_36,plain,
( lt(X2,X3)
| ~ strictorderedP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_15]),c_0_21])]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
lt(esk53_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_41,plain,
( lt(X1,X2)
| ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_24]),c_0_26]),c_0_28])]) ).
cnf(c_0_43,negated_conjecture,
strictorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_44,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_38,c_0_11]) ).
cnf(c_0_45,negated_conjecture,
~ lt(esk52_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_28]),c_0_21])]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]),c_0_26]),c_0_15]),c_0_16]),c_0_28]),c_0_21])]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC305+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
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:43:02 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.59/1.80 % Version : CSE_E---1.7
% 1.59/1.80 % Problem : theBenchmark.p
% 1.59/1.80 % SZS status Theorem for theBenchmark.p
% 1.59/1.80 % SZS output start CNFRefutation
% See solution above
% 1.59/1.81 % Total time : 1.373s
%------------------------------------------------------------------------------