%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC386+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 : n009.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 05:19:27 PM UTC 2026
% Result : Theorem 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 132 ( 59 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 151 ( 53 ~; 59 |; 24 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 26 ( 0 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& ( nil != X4
| nil != X3 ) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X1
& memberP(X2,X6) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/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
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& ( nil != X4
| nil != X3 ) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X1
& memberP(X2,X6) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_5,negated_conjecture,
! [X465] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( nil = esk51_0
| ssItem(esk52_0) )
& ( nil = esk50_0
| ssItem(esk52_0) )
& ( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk52_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk52_0) )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssItem(X465)
| cons(X465,nil) != esk48_0
| ~ memberP(esk49_0,X465)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssItem(X465)
| cons(X465,nil) != esk48_0
| ~ memberP(esk49_0,X465)
| 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_4])])])])]) ).
cnf(c_0_6,negated_conjecture,
( nil = esk49_0
| ~ ssItem(X1)
| cons(X1,nil) != esk48_0
| ~ memberP(esk49_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( nil = esk51_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( nil = esk51_0
| memberP(esk51_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_13,negated_conjecture,
( nil = esk50_0
| memberP(esk51_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( esk49_0 = nil
| cons(X1,nil) != esk50_0
| ~ memberP(esk49_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( cons(esk52_0,nil) = esk50_0
| esk49_0 = nil ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( esk49_0 = nil
| ssItem(esk52_0) ),
inference(rw,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( esk49_0 = nil
| memberP(esk49_0,esk52_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_9]),c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_19,plain,
! [X366] :
( ~ ssItem(X366)
| ~ memberP(nil,X366) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_20,negated_conjecture,
( esk50_0 = nil
| memberP(esk49_0,esk52_0) ),
inference(rw,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_21,negated_conjecture,
esk49_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
fof(c_0_22,plain,
! [X318,X319] :
( ( ~ neq(X318,X319)
| X318 != X319
| ~ ssList(X319)
| ~ ssList(X318) )
& ( X318 = X319
| neq(X318,X319)
| ~ ssList(X319)
| ~ ssList(X318) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_23,negated_conjecture,
( neq(esk49_0,nil)
| esk50_0 != nil ),
inference(rw,[status(thm)],[c_0_18,c_0_7]) ).
cnf(c_0_24,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( esk50_0 = nil
| memberP(nil,esk52_0) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( nil = esk50_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_27,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( neq(nil,nil)
| esk50_0 != nil ),
inference(rw,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_32,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC386+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 : n009.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 04:47:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------