%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC030+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 : n001.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 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 126 ( 83 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 131 ( 46 ~; 50 |; 18 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X5,X6) != X4
| app(X6,X5) != X3 ) ) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X5,X6) != X4
| app(X6,X5) != X3 ) ) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& ssList(esk53_0)
& app(esk52_0,esk53_0) = esk51_0
& app(esk53_0,esk52_0) = esk50_0
& ( 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_5])])])]) ).
fof(c_0_7,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_8,negated_conjecture,
app(esk52_0,esk53_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
app(esk52_0,esk53_0) = esk49_0,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( esk53_0 = nil
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_15,negated_conjecture,
( nil = esk48_0
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
app(esk53_0,esk52_0) = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_18,plain,
! [X436] :
( ~ ssList(X436)
| app(X436,nil) = X436 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_19,negated_conjecture,
( esk48_0 = nil
| esk53_0 = nil ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X344] :
( ~ ssList(X344)
| app(nil,X344) = X344 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_21,negated_conjecture,
app(esk53_0,esk52_0) = esk48_0,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( app(esk52_0,nil) = esk49_0
| esk48_0 = nil ),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_24,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( app(nil,esk52_0) = esk48_0
| esk48_0 = nil ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( esk48_0 = nil
| esk52_0 = esk49_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_12])]) ).
cnf(c_0_27,negated_conjecture,
( esk48_0 = nil
| esk52_0 = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_12])]) ).
cnf(c_0_28,negated_conjecture,
( esk49_0 = esk48_0
| esk48_0 = nil ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( esk52_0 = nil
| esk48_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_21]),c_0_13]),c_0_12])]) ).
cnf(c_0_30,negated_conjecture,
esk48_0 = nil,
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
esk52_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_32,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
app(esk53_0,nil) = nil,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_30]),c_0_31]) ).
cnf(c_0_34,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_35,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_36,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_37,negated_conjecture,
esk53_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_13])]) ).
cnf(c_0_38,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_35])]),c_0_34])]) ).
cnf(c_0_39,negated_conjecture,
esk49_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_30])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_31]),c_0_37]),c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC030+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
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 04:20:03 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % 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 : 1.372s
%------------------------------------------------------------------------------