%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC419+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 : n027.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 05:19:36 PM UTC 2026
% Result : Theorem 1.46s 1.77s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 117 ( 43 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 137 ( 54 ~; 47 |; 24 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X4
| app(X9,cons(X8,nil)) != X3 ) )
& neq(X4,nil) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
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] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X4
| app(X9,cons(X8,nil)) != X3 ) )
& neq(X4,nil) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_6,negated_conjecture,
! [X470,X471,X472] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ( ~ ssItem(X470)
| ~ ssList(X471)
| ~ ssList(X472)
| app(app(X471,cons(X470,nil)),X472) != esk49_0
| app(app(X472,cons(X470,nil)),X471) != esk48_0 )
& ( nil = esk50_0
| nil != esk51_0 )
& ( ssItem(esk52_0)
| ~ neq(esk51_0,nil) )
& ( ssList(esk53_0)
| ~ neq(esk51_0,nil) )
& ( app(cons(esk52_0,nil),esk53_0) = esk51_0
| ~ neq(esk51_0,nil) )
& ( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) ) ),
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),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(app(X3,cons(X1,nil)),X2) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk50_0
| app(app(X3,cons(X2,nil)),X1) != esk51_0
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).
cnf(c_0_16,negated_conjecture,
app(esk53_0,cons(esk52_0,nil)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12])]) ).
cnf(c_0_18,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12])]) ).
fof(c_0_19,plain,
! [X442] :
( ~ ssList(X442)
| app(X442,nil) = X442 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( app(app(X1,cons(esk52_0,nil)),esk53_0) != esk51_0
| app(esk50_0,X1) != esk50_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_22,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_20,c_0_10]) ).
fof(c_0_25,plain,
! [X350] :
( ~ ssList(X350)
| app(nil,X350) = X350 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_26,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
app(app(nil,cons(esk52_0,nil)),esk53_0) != esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_28,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
app(cons(esk52_0,nil),esk53_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_12])]) ).
fof(c_0_30,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| ssList(cons(X327,X326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_31,negated_conjecture,
~ ssList(cons(esk52_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_32,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC419+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
% 0.16/0.33 % Computer : n027.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 04:49:35 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.46/1.77 % Version : CSE_E---1.7
% 1.46/1.77 % Problem : theBenchmark.p
% 1.46/1.77 % SZS status Theorem for theBenchmark.p
% 1.46/1.77 % SZS output start CNFRefutation
% See solution above
% 1.46/1.78 % Total time : 1.372s
%------------------------------------------------------------------------------