%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC002+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 : 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 05:17:50 PM UTC 2026
% Result : Theorem 1.42s 1.76s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 237 ( 69 equ)
% Maximal formula atoms : 96 ( 7 avg)
% Number of connectives : 342 ( 138 ~; 143 |; 45 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 20 !; 8 ?)
% 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)
=> ( ~ memberP(X2,X8)
| ~ geq(X8,X5)
| X5 = X8 ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(app(X10,cons(X9,nil)),X11) != X4
| app(X10,X11) != X3
| ? [X12] :
( ssItem(X12)
& X9 != X12
& memberP(X4,X12)
& geq(X12,X9) ) ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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(X6,X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X2,X8)
| ~ geq(X8,X5)
| X5 = X8 ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(app(X10,cons(X9,nil)),X11) != X4
| app(X10,X11) != X3
| ? [X12] :
( ssItem(X12)
& X9 != X12
& memberP(X4,X12)
& geq(X12,X9) ) ) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_2,negated_conjecture,
! [X476,X477,X478,X483] :
( 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(esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ~ neq(esk51_0,nil)
| ssItem(esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( neq(esk49_0,nil)
| memberP(esk49_0,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ~ neq(esk51_0,nil)
| memberP(esk49_0,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( neq(esk49_0,nil)
| geq(esk52_3(X476,X477,X478),X476)
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ~ neq(esk51_0,nil)
| geq(esk52_3(X476,X477,X478),X476)
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( neq(esk49_0,nil)
| X476 != esk52_3(X476,X477,X478)
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ~ neq(esk51_0,nil)
| X476 != esk52_3(X476,X477,X478)
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk49_0
| app(X477,X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( neq(esk49_0,nil)
| ssItem(esk53_0) )
& ( ~ neq(esk51_0,nil)
| ssItem(esk53_0) )
& ( neq(esk49_0,nil)
| ssList(esk54_0) )
& ( ~ neq(esk51_0,nil)
| ssList(esk54_0) )
& ( neq(esk49_0,nil)
| ssList(esk55_0) )
& ( ~ neq(esk51_0,nil)
| ssList(esk55_0) )
& ( neq(esk49_0,nil)
| app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk51_0 )
& ( ~ neq(esk51_0,nil)
| app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk51_0 )
& ( neq(esk49_0,nil)
| app(esk54_0,esk55_0) = esk50_0 )
& ( ~ neq(esk51_0,nil)
| app(esk54_0,esk55_0) = esk50_0 )
& ( neq(esk49_0,nil)
| ~ ssItem(X483)
| esk53_0 = X483
| ~ memberP(esk51_0,X483)
| ~ geq(X483,esk53_0) )
& ( ~ neq(esk51_0,nil)
| ~ ssItem(X483)
| esk53_0 = X483
| ~ memberP(esk51_0,X483)
| ~ geq(X483,esk53_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(esk49_0,nil),
inference(cn,[status(thm)],[c_0_3]) ).
cnf(c_0_5,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( memberP(esk49_0,esk52_3(X1,X2,X3))
| ~ neq(esk51_0,nil)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(X2,X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( app(esk54_0,esk55_0) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
( ssList(esk55_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_12,negated_conjecture,
( ssList(esk54_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( ssItem(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_14,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ neq(esk51_0,nil)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(X2,X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( ~ neq(esk51_0,nil)
| X1 != esk52_3(X1,X2,X3)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(X2,X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_16,negated_conjecture,
( esk53_0 = X1
| ~ neq(esk51_0,nil)
| ~ ssItem(X1)
| ~ memberP(esk51_0,X1)
| ~ geq(X1,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_17,negated_conjecture,
( memberP(esk51_0,esk52_3(X1,X2,X3))
| app(app(X2,cons(X1,nil)),X3) != esk51_0
| app(X2,X3) != esk48_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_5]),c_0_5]),c_0_7])]) ).
cnf(c_0_18,negated_conjecture,
app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_7])]) ).
cnf(c_0_19,negated_conjecture,
app(esk54_0,esk55_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_7])]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_7])]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_7])]) ).
cnf(c_0_22,negated_conjecture,
ssItem(esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_7])]) ).
cnf(c_0_23,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| app(app(X2,cons(X1,nil)),X3) != esk51_0
| app(X2,X3) != esk48_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_5]),c_0_7])]) ).
cnf(c_0_24,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk51_0
| esk52_3(X2,X1,X3) != X2
| 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_15,c_0_5]),c_0_7])]) ).
cnf(c_0_25,negated_conjecture,
( geq(esk52_3(X1,X2,X3),X1)
| ~ neq(esk51_0,nil)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(X2,X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_26,negated_conjecture,
( esk53_0 = X1
| ~ geq(X1,esk53_0)
| ~ memberP(esk51_0,X1)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_7])]) ).
cnf(c_0_27,negated_conjecture,
memberP(esk51_0,esk52_3(esk53_0,esk54_0,esk55_0)),
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_17,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_28,negated_conjecture,
ssItem(esk52_3(esk53_0,esk54_0,esk55_0)),
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_23,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
esk52_3(esk53_0,esk54_0,esk55_0) != esk53_0,
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_24,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_30,negated_conjecture,
( geq(esk52_3(X1,X2,X3),X1)
| app(app(X2,cons(X1,nil)),X3) != esk51_0
| app(X2,X3) != esk48_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_5]),c_0_7])]) ).
cnf(c_0_31,negated_conjecture,
~ geq(esk52_3(esk53_0,esk54_0,esk55_0),esk53_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_30,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC002+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
% 0.16/0.32 % 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
% 0.16/0.33 % DateTime : Tue May 5 04:16:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.42/1.76 % Version : CSE_E---1.7
% 1.42/1.76 % Problem : theBenchmark.p
% 1.42/1.76 % SZS status Theorem for theBenchmark.p
% 1.42/1.76 % SZS output start CNFRefutation
% See solution above
% 1.42/1.76 % Total time : 1.373s
%------------------------------------------------------------------------------