%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC320+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 05:19:10 PM UTC 2026
% Result : Theorem 1.36s 1.73s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 136 ( 65 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 168 ( 64 ~; 66 |; 27 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 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 : 29 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) != X4 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X1
& app(X8,cons(X7,nil)) = X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) != X4 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X1
& app(X8,cons(X7,nil)) = X2 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_4,negated_conjecture,
! [X470,X471] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_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) = esk50_0
| ~ neq(esk51_0,nil) )
& ( app(esk53_0,cons(esk52_0,nil)) = esk51_0
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssItem(X470)
| ~ ssList(X471)
| app(cons(X470,nil),X471) != esk48_0
| app(X471,cons(X470,nil)) != esk49_0
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssItem(X470)
| ~ ssList(X471)
| app(cons(X470,nil),X471) != esk48_0
| app(X471,cons(X470,nil)) != esk49_0
| nil != esk48_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_3])])])])]) ).
cnf(c_0_5,negated_conjecture,
( neq(esk49_0,nil)
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_6,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
( nil = esk49_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk48_0
| app(X2,cons(X1,nil)) != esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( esk51_0 = nil
| neq(esk51_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk48_0
| ~ neq(esk51_0,nil) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_15,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( esk51_0 = nil
| app(X1,cons(X2,nil)) != esk51_0
| app(cons(X2,nil),X1) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_6]),c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk51_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( esk51_0 = nil
| ssItem(esk52_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( esk51_0 = nil
| ssList(esk53_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk48_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
fof(c_0_21,plain,
! [X322,X323] :
( ( ~ neq(X322,X323)
| X322 != X323
| ~ ssList(X323)
| ~ ssList(X322) )
& ( X322 = X323
| neq(X322,X323)
| ~ ssList(X323)
| ~ ssList(X322) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_22,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,negated_conjecture,
( esk48_0 = nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_24,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_25,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( neq(esk51_0,nil)
| esk48_0 != nil ),
inference(rw,[status(thm)],[c_0_22,c_0_6]) ).
cnf(c_0_27,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_24]),c_0_27])]) ).
cnf(c_0_30,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC320+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
% 0.17/0.33 % Computer : n018.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 04:43:47 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % 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 : 1.370s
%------------------------------------------------------------------------------