%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC012+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 : n031.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 05:17:53 PM UTC 2026
% Result : Theorem 1.31s 1.72s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 98 ( 31 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 118 ( 43 ~; 41 |; 23 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(X6,X7) = X1 ) ) )
| ! [X8] :
( ssItem(X8)
=> app(X3,cons(X8,nil)) != X4 ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/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
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(X6,X7) = X1 ) ) )
| ! [X8] :
( ssItem(X8)
=> app(X3,cons(X8,nil)) != X4 ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_4,negated_conjecture,
! [X468,X469,X470] :
( 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(esk49_0,nil) )
& ( ~ neq(esk51_0,nil)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ ssItem(X468)
| ~ ssList(X469)
| ~ ssList(X470)
| app(app(X469,cons(X468,nil)),X470) != esk49_0
| app(X469,X470) != esk48_0 )
& ( ~ neq(esk51_0,nil)
| ~ ssItem(X468)
| ~ ssList(X469)
| ~ ssList(X470)
| app(app(X469,cons(X468,nil)),X470) != esk49_0
| app(X469,X470) != esk48_0 )
& ( neq(esk49_0,nil)
| ssItem(esk52_0) )
& ( ~ neq(esk51_0,nil)
| ssItem(esk52_0) )
& ( neq(esk49_0,nil)
| app(esk50_0,cons(esk52_0,nil)) = esk51_0 )
& ( ~ neq(esk51_0,nil)
| app(esk50_0,cons(esk52_0,nil)) = esk51_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)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_6,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(X2,X3) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X440] :
( ~ ssList(X440)
| app(X440,nil) = X440 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_10,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk49_0
| app(X1,X3) != esk48_0
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
cnf(c_0_11,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( app(esk50_0,cons(esk52_0,nil)) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( app(app(esk48_0,cons(X1,nil)),nil) != esk49_0
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[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_18,negated_conjecture,
app(esk48_0,cons(esk52_0,nil)) = esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_7]),c_0_7]),c_0_8])]) ).
cnf(c_0_19,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_7]),c_0_8])]) ).
cnf(c_0_20,negated_conjecture,
app(esk49_0,nil) != esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_11]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC012+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.16/0.32 % Computer : n031.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 04:15:23 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.31/1.72 % Version : CSE_E---1.7
% 1.31/1.72 % Problem : theBenchmark.p
% 1.31/1.72 % SZS status Theorem for theBenchmark.p
% 1.31/1.72 % SZS output start CNFRefutation
% See solution above
% 1.31/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------