%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC422+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 : n004.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 05:19:36 PM UTC 2026
% Result : Theorem 1.34s 1.73s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 112 ( 32 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 138 ( 46 ~; 49 |; 29 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 17 !; 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(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X4
| app(app(X10,cons(X8,nil)),X9) != X3 ) ) ) ) )
& ( ~ 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)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X4
| app(app(X10,cons(X8,nil)),X9) != X3 ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_2,negated_conjecture,
! [X472,X473,X474] :
( 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(X472)
| ~ ssList(X473)
| ~ ssList(X474)
| app(app(X473,cons(X472,nil)),X474) != esk49_0
| app(app(X474,cons(X472,nil)),X473) != esk48_0 )
& ( ~ neq(esk51_0,nil)
| ~ ssItem(X472)
| ~ ssList(X473)
| ~ ssList(X474)
| app(app(X473,cons(X472,nil)),X474) != esk49_0
| app(app(X474,cons(X472,nil)),X473) != esk48_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)
| ssList(esk54_0) )
& ( ~ neq(esk51_0,nil)
| ssList(esk54_0) )
& ( neq(esk49_0,nil)
| app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk51_0 )
& ( ~ neq(esk51_0,nil)
| app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk51_0 )
& ( neq(esk49_0,nil)
| app(app(esk54_0,cons(esk52_0,nil)),esk53_0) = esk50_0 )
& ( ~ neq(esk51_0,nil)
| app(app(esk54_0,cons(esk52_0,nil)),esk53_0) = esk50_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)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(app(X3,cons(X1,nil)),X2) != esk48_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,
( app(app(esk54_0,cons(esk52_0,nil)),esk53_0) = 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,
( app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( ssList(esk54_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_12,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk48_0
| app(app(X3,cons(X2,nil)),X1) != esk49_0
| ~ ssList(X1)
| ~ ssList(X3)
| ~ 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_14,negated_conjecture,
app(app(esk54_0,cons(esk52_0,nil)),esk53_0) = 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_15,negated_conjecture,
app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_5]),c_0_5]),c_0_6])]) ).
cnf(c_0_16,negated_conjecture,
ssList(esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,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_11,c_0_5]),c_0_6])]) ).
cnf(c_0_18,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_5]),c_0_6])]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC422+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
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 04:50:02 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % 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
% 1.34/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------