%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC029+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 : n023.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 05:17:58 PM UTC 2026
% Result : Theorem 1.34s 1.73s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 153 ( 75 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 184 ( 72 ~; 66 |; 24 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 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 : 38 ( 0 sgn 28 !; 0 ?)
% 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) != X4
| app(X6,cons(X5,nil)) != X3 ) ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| 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(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(c_0_6,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) != X4
| app(X6,cons(X5,nil)) != X3 ) ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_7,negated_conjecture,
( 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) = esk51_0
| ~ neq(esk51_0,nil) )
& ( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) )
& ( nil = esk48_0
| nil = esk49_0 )
& ( nil != esk49_0
| nil = esk49_0 )
& ( nil = esk48_0
| nil != esk48_0 )
& ( nil != esk49_0
| nil != esk48_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_8,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( esk48_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( nil = esk48_0
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
esk51_0 != nil,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
esk48_0 = nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_9]),c_0_14]) ).
fof(c_0_17,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_18,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_19,plain,
! [X434,X435] :
( ( nil = X435
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil = X434
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil != X435
| nil != X434
| nil = app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_20,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = nil
| ~ neq(esk51_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11]),c_0_16]) ).
cnf(c_0_21,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_24,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
app(esk53_0,cons(esk52_0,nil)) = nil,
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_22]),c_0_23])]),c_0_14]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk53_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_22]),c_0_23])]),c_0_14]) ).
fof(c_0_28,plain,
! [X320,X321] :
( ~ ssList(X320)
| ~ ssItem(X321)
| ssList(cons(X321,X320)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_29,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,negated_conjecture,
( esk53_0 = nil
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
ssItem(esk52_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_22]),c_0_23])]),c_0_14]) ).
cnf(c_0_33,negated_conjecture,
esk53_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_22]),c_0_32])]) ).
cnf(c_0_34,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_35,negated_conjecture,
app(nil,cons(esk52_0,nil)) = nil,
inference(rw,[status(thm)],[c_0_26,c_0_33]) ).
fof(c_0_36,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| cons(X323,X322) != X322 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_37,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_34,c_0_35]),c_0_22])]) ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,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_37,c_0_31]),c_0_22]),c_0_32])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC029+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 : n023.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 04:17:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.73 % Version : CSE_E---1.7
% 1.34/1.73 % Problem : theBenchmark.p
% 1.34/1.73 % SZS status Theorem for theBenchmark.p
% 1.34/1.73 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------