%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC096+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 : n024.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 05:18:15 PM UTC 2026
% Result : Theorem 1.13s 1.62s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 99 ( 33 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 126 ( 46 ~; 47 |; 25 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 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 : 23 ( 0 sgn 14 !; 4 ?)
% 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)
& cons(X5,nil) = X1
& app(X6,cons(X5,nil)) = X2 ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| cons(X7,nil) != X3
| app(X8,cons(X7,nil)) != X4 ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(c_0_1,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)
& cons(X5,nil) = X1
& app(X6,cons(X5,nil)) = X2 ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| cons(X7,nil) != X3
| app(X8,cons(X7,nil)) != X4 ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_2,negated_conjecture,
! [X468,X469] :
( 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)
| cons(X468,nil) != esk48_0
| app(X469,cons(X468,nil)) != esk49_0 )
& ( ~ neq(esk51_0,nil)
| ~ ssItem(X468)
| ~ ssList(X469)
| cons(X468,nil) != esk48_0
| app(X469,cons(X468,nil)) != esk49_0 )
& ( neq(esk49_0,nil)
| ssItem(esk52_0) )
& ( ~ neq(esk51_0,nil)
| ssItem(esk52_0) )
& ( neq(esk49_0,nil)
| ssList(esk53_0) )
& ( ~ neq(esk51_0,nil)
| ssList(esk53_0) )
& ( neq(esk49_0,nil)
| cons(esk52_0,nil) = esk50_0 )
& ( ~ neq(esk51_0,nil)
| cons(esk52_0,nil) = esk50_0 )
& ( neq(esk49_0,nil)
| app(esk53_0,cons(esk52_0,nil)) = esk51_0 )
& ( ~ neq(esk51_0,nil)
| app(esk53_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_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,nil) != esk48_0
| app(X2,cons(X1,nil)) != esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_3]) ).
cnf(c_0_7,negated_conjecture,
( cons(esk52_0,nil) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( app(X1,cons(X2,nil)) != esk49_0
| cons(X2,nil) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_6])]) ).
cnf(c_0_11,negated_conjecture,
cons(esk52_0,nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_5]),c_0_6])]) ).
cnf(c_0_12,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_5]),c_0_6])]) ).
cnf(c_0_13,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_14,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( app(X1,esk48_0) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_16,negated_conjecture,
app(esk53_0,esk48_0) = esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_5]),c_0_5]),c_0_6])]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_5]),c_0_6])]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC096+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 23:25:11 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.13/1.62 % Version : CSE_E---1.7
% 1.13/1.62 % Problem : theBenchmark.p
% 1.13/1.62 % SZS status Theorem for theBenchmark.p
% 1.13/1.62 % SZS output start CNFRefutation
% See solution above
% 1.13/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------