%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC217+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 : n004.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 05:18:46 PM UTC 2026
% Result : Theorem 1.33s 1.72s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 87 ( 27 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 101 ( 39 ~; 31 |; 16 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| neq(X1,nil)
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& neq(X4,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
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_4,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| neq(X1,nil)
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_5,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)
& ~ neq(esk48_0,nil)
& ( nil = esk50_0
| nil != esk51_0 )
& ( ssItem(esk52_0)
| ~ neq(esk51_0,nil) )
& ( cons(esk52_0,nil) = esk50_0
| ~ neq(esk51_0,nil) )
& ( memberP(esk51_0,esk52_0)
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_6,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X321,X322] :
( ~ ssList(X321)
| ~ ssItem(X322)
| cons(X322,X321) != X321 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_9,negated_conjecture,
( cons(esk52_0,nil) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
~ neq(esk48_0,nil),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,plain,
! [X317,X318] :
( ( ~ neq(X317,X318)
| X317 != X318
| ~ ssList(X318)
| ~ ssList(X317) )
& ( X317 = X318
| neq(X317,X318)
| ~ ssList(X318)
| ~ ssList(X317) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
cons(esk52_0,nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).
cnf(c_0_18,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_19,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10])]) ).
cnf(c_0_20,negated_conjecture,
~ neq(esk50_0,nil),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_23,negated_conjecture,
esk50_0 != 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_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC217+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 : n004.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 04:34:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.72 % Version : CSE_E---1.7
% 1.33/1.72 % Problem : theBenchmark.p
% 1.33/1.72 % SZS status Theorem for theBenchmark.p
% 1.33/1.72 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------