%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC003+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 : n025.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 05:17:51 PM UTC 2026
% Result : Theorem 1.36s 1.73s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 0 def)
% Number of atoms : 182 ( 46 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 231 ( 86 ~; 84 |; 40 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X4
| app(X9,X10) != X3
| ? [X11] :
( ssItem(X11)
& X8 != X11
& memberP(X4,X11)
& geq(X11,X8) ) ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X4
| app(X9,X10) != X3
| ? [X11] :
( ssItem(X11)
& X8 != X11
& memberP(X4,X11)
& geq(X11,X8) ) ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_6,negated_conjecture,
! [X474,X475,X476,X480] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( neq(esk49_0,nil)
| neq(esk49_0,nil) )
& ( ~ neq(esk51_0,nil)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ ssList(X474)
| ~ ssList(X475)
| ~ ssList(X476)
| app(app(X474,X475),X476) != esk49_0
| app(X474,X476) != esk48_0
| ~ neq(X475,nil) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X474)
| ~ ssList(X475)
| ~ ssList(X476)
| app(app(X474,X475),X476) != esk49_0
| app(X474,X476) != esk48_0
| ~ neq(X475,nil) )
& ( neq(esk49_0,nil)
| ssItem(esk52_0) )
& ( ~ neq(esk51_0,nil)
| ssItem(esk52_0) )
& ( neq(esk49_0,nil)
| ssList(esk53_0) )
& ( ~ neq(esk51_0,nil)
| ssList(esk53_0) )
& ( neq(esk49_0,nil)
| ssList(esk54_0) )
& ( ~ neq(esk51_0,nil)
| ssList(esk54_0) )
& ( neq(esk49_0,nil)
| app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk51_0 )
& ( ~ neq(esk51_0,nil)
| app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk51_0 )
& ( neq(esk49_0,nil)
| app(esk53_0,esk54_0) = esk50_0 )
& ( ~ neq(esk51_0,nil)
| app(esk53_0,esk54_0) = esk50_0 )
& ( neq(esk49_0,nil)
| ~ ssItem(X480)
| esk52_0 = X480
| ~ memberP(esk51_0,X480)
| ~ geq(X480,esk52_0) )
& ( ~ neq(esk51_0,nil)
| ~ ssItem(X480)
| esk52_0 = X480
| ~ memberP(esk51_0,X480)
| ~ geq(X480,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_5])])])])]) ).
cnf(c_0_7,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X1,X2),X3) != esk49_0
| app(X1,X3) != esk48_0
| ~ neq(X2,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( app(esk53_0,esk54_0) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( ssList(esk54_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( app(app(X1,X2),X3) != esk51_0
| app(X1,X3) != esk48_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_9]),c_0_11])]) ).
cnf(c_0_17,negated_conjecture,
app(esk53_0,esk54_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_11])]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_11])]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11])]) ).
cnf(c_0_20,negated_conjecture,
( app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( app(app(esk53_0,X1),esk54_0) != esk51_0
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_22,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_11])]) ).
fof(c_0_23,plain,
! [X330,X331] :
( ~ ssList(X330)
| ~ ssItem(X331)
| ssList(cons(X331,X330)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_24,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ neq(cons(esk52_0,nil),nil) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_28,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_11])]) ).
fof(c_0_29,plain,
! [X328,X329] :
( ( ~ neq(X328,X329)
| X328 != X329
| ~ ssList(X329)
| ~ ssList(X328) )
& ( X328 = X329
| neq(X328,X329)
| ~ ssList(X329)
| ~ ssList(X328) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_30,negated_conjecture,
~ neq(cons(esk52_0,nil),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_31,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_32,plain,
! [X332,X333] :
( ~ ssList(X332)
| ~ ssItem(X333)
| cons(X333,X332) != X332 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_33,negated_conjecture,
( cons(esk52_0,nil) = nil
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_27])]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
cons(esk52_0,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC003+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
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:14:43 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.36/1.73 % Version : CSE_E---1.7
% 1.36/1.73 % Problem : theBenchmark.p
% 1.36/1.73 % SZS status Theorem for theBenchmark.p
% 1.36/1.73 % SZS output start CNFRefutation
% See solution above
% 1.36/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------