%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC412+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 : n002.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 05:19:34 PM UTC 2026
% Result : Theorem 6.54s 4.56s
% Output : CNFRefutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 56 ( 12 unt; 0 def)
% Number of atoms : 384 ( 122 equ)
% Maximal formula atoms : 156 ( 6 avg)
% Number of connectives : 509 ( 181 ~; 235 |; 71 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 64 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 32 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(app(cons(X5,nil),cons(X6,nil)),X7) = X4 ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> app(app(cons(X8,nil),cons(X9,nil)),X10) != X2 ) ) ) )
& ( ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(app(cons(X12,nil),X13),cons(X11,nil)) != X3
& app(app(cons(X11,nil),X13),cons(X12,nil)) = X4 ) ) )
| ! [X14] :
( ssItem(X14)
=> ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssList(X16)
=> app(app(cons(X14,nil),cons(X15,nil)),X16) != X2 ) ) )
| ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ~ ssList(X19)
| app(app(cons(X17,nil),X19),cons(X18,nil)) != X2
| app(app(cons(X18,nil),X19),cons(X17,nil)) = X1 ) ) ) ) ) ) ) ) ),
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
| ( ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(app(cons(X5,nil),cons(X6,nil)),X7) = X4 ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> app(app(cons(X8,nil),cons(X9,nil)),X10) != X2 ) ) ) )
& ( ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(app(cons(X12,nil),X13),cons(X11,nil)) != X3
& app(app(cons(X11,nil),X13),cons(X12,nil)) = X4 ) ) )
| ! [X14] :
( ssItem(X14)
=> ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssList(X16)
=> app(app(cons(X14,nil),cons(X15,nil)),X16) != X2 ) ) )
| ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ~ ssList(X19)
| app(app(cons(X17,nil),X19),cons(X18,nil)) != X2
| app(app(cons(X18,nil),X19),cons(X17,nil)) = X1 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_2,negated_conjecture,
! [X490,X491,X492,X496,X497,X498] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssItem(X496)
| ~ ssItem(X497)
| ~ ssList(X498)
| app(app(cons(X497,nil),X498),cons(X496,nil)) = esk50_0
| app(app(cons(X496,nil),X498),cons(X497,nil)) != esk51_0
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( ssItem(esk55_0)
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( ssItem(esk56_0)
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( ssList(esk57_0)
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( app(app(cons(esk55_0,nil),cons(esk56_0,nil)),esk57_0) = esk49_0
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( ssItem(esk58_0)
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( ssItem(esk59_0)
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( ssList(esk60_0)
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0
| ~ ssItem(X490)
| ~ ssItem(X491)
| ~ ssList(X492)
| app(app(cons(X490,nil),cons(X491,nil)),X492) != esk51_0 )
& ( ~ ssItem(X496)
| ~ ssItem(X497)
| ~ ssList(X498)
| app(app(cons(X497,nil),X498),cons(X496,nil)) = esk50_0
| app(app(cons(X496,nil),X498),cons(X497,nil)) != esk51_0
| ssItem(esk52_0) )
& ( ssItem(esk55_0)
| ssItem(esk52_0) )
& ( ssItem(esk56_0)
| ssItem(esk52_0) )
& ( ssList(esk57_0)
| ssItem(esk52_0) )
& ( app(app(cons(esk55_0,nil),cons(esk56_0,nil)),esk57_0) = esk49_0
| ssItem(esk52_0) )
& ( ssItem(esk58_0)
| ssItem(esk52_0) )
& ( ssItem(esk59_0)
| ssItem(esk52_0) )
& ( ssList(esk60_0)
| ssItem(esk52_0) )
& ( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ssItem(esk52_0) )
& ( app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0
| ssItem(esk52_0) )
& ( ~ ssItem(X496)
| ~ ssItem(X497)
| ~ ssList(X498)
| app(app(cons(X497,nil),X498),cons(X496,nil)) = esk50_0
| app(app(cons(X496,nil),X498),cons(X497,nil)) != esk51_0
| ssItem(esk53_0) )
& ( ssItem(esk55_0)
| ssItem(esk53_0) )
& ( ssItem(esk56_0)
| ssItem(esk53_0) )
& ( ssList(esk57_0)
| ssItem(esk53_0) )
& ( app(app(cons(esk55_0,nil),cons(esk56_0,nil)),esk57_0) = esk49_0
| ssItem(esk53_0) )
& ( ssItem(esk58_0)
| ssItem(esk53_0) )
& ( ssItem(esk59_0)
| ssItem(esk53_0) )
& ( ssList(esk60_0)
| ssItem(esk53_0) )
& ( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ssItem(esk53_0) )
& ( app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0
| ssItem(esk53_0) )
& ( ~ ssItem(X496)
| ~ ssItem(X497)
| ~ ssList(X498)
| app(app(cons(X497,nil),X498),cons(X496,nil)) = esk50_0
| app(app(cons(X496,nil),X498),cons(X497,nil)) != esk51_0
| ssList(esk54_0) )
& ( ssItem(esk55_0)
| ssList(esk54_0) )
& ( ssItem(esk56_0)
| ssList(esk54_0) )
& ( ssList(esk57_0)
| ssList(esk54_0) )
& ( app(app(cons(esk55_0,nil),cons(esk56_0,nil)),esk57_0) = esk49_0
| ssList(esk54_0) )
& ( ssItem(esk58_0)
| ssList(esk54_0) )
& ( ssItem(esk59_0)
| ssList(esk54_0) )
& ( ssList(esk60_0)
| ssList(esk54_0) )
& ( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ssList(esk54_0) )
& ( app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0
| ssList(esk54_0) )
& ( ~ ssItem(X496)
| ~ ssItem(X497)
| ~ ssList(X498)
| app(app(cons(X497,nil),X498),cons(X496,nil)) = esk50_0
| app(app(cons(X496,nil),X498),cons(X497,nil)) != esk51_0
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( ssItem(esk55_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( ssItem(esk56_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( ssList(esk57_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( app(app(cons(esk55_0,nil),cons(esk56_0,nil)),esk57_0) = esk49_0
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( ssItem(esk58_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( ssItem(esk59_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( ssList(esk60_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 )
& ( app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_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,
( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( ssList(esk60_0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( ssItem(esk59_0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( ssItem(esk58_0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
( app(app(cons(X2,nil),X3),cons(X1,nil)) = esk50_0
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk49_0
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_12,negated_conjecture,
( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_14,negated_conjecture,
( app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0
| ssList(esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( ssList(esk60_0)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk49_0
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( ssList(esk60_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_17,negated_conjecture,
( ssList(esk60_0)
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_18,negated_conjecture,
( ssList(esk60_0)
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_19,negated_conjecture,
( ssList(esk60_0)
| ssList(esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_20,negated_conjecture,
( ssItem(esk59_0)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk49_0
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_21,negated_conjecture,
( ssItem(esk59_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_22,negated_conjecture,
( ssItem(esk59_0)
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_23,negated_conjecture,
( ssItem(esk59_0)
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_24,negated_conjecture,
( ssItem(esk59_0)
| ssList(esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_25,negated_conjecture,
( ssItem(esk58_0)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk49_0
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_26,negated_conjecture,
( ssItem(esk58_0)
| app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_27,negated_conjecture,
( ssItem(esk58_0)
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_28,negated_conjecture,
( ssItem(esk58_0)
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_29,negated_conjecture,
( ssItem(esk58_0)
| ssList(esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_30,negated_conjecture,
( app(app(cons(X2,nil),X3),cons(X1,nil)) = esk50_0
| ssList(esk54_0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_31,negated_conjecture,
( app(app(cons(X2,nil),X3),cons(X1,nil)) = esk50_0
| ssItem(esk53_0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_32,negated_conjecture,
( app(app(cons(X2,nil),X3),cons(X1,nil)) = esk50_0
| ssItem(esk52_0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_33,negated_conjecture,
( app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_34,negated_conjecture,
( app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0
| app(app(cons(X1,nil),X2),cons(X3,nil)) = esk48_0
| app(app(cons(X3,nil),X2),cons(X1,nil)) != esk49_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_4]) ).
cnf(c_0_35,negated_conjecture,
app(app(cons(esk58_0,nil),esk60_0),cons(esk59_0,nil)) = esk49_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk60_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_37,negated_conjecture,
ssItem(esk59_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_38,negated_conjecture,
ssItem(esk58_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]),c_0_29]) ).
cnf(c_0_39,negated_conjecture,
( app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0
| app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_40,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = esk48_0
| ssList(esk54_0)
| app(app(cons(X3,nil),X2),cons(X1,nil)) != esk49_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_9]),c_0_4]) ).
cnf(c_0_41,negated_conjecture,
( ssList(esk54_0)
| app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_42,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = esk48_0
| ssItem(esk53_0)
| app(app(cons(X3,nil),X2),cons(X1,nil)) != esk49_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_9]),c_0_4]) ).
cnf(c_0_43,negated_conjecture,
( ssItem(esk53_0)
| app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_44,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = esk48_0
| ssItem(esk52_0)
| app(app(cons(X3,nil),X2),cons(X1,nil)) != esk49_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_9]),c_0_4]) ).
cnf(c_0_45,negated_conjecture,
( ssItem(esk52_0)
| app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_46,negated_conjecture,
( app(app(cons(X2,nil),X3),cons(X1,nil)) = esk50_0
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(app(cons(X1,nil),X3),cons(X2,nil)) != esk51_0
| ~ ssItem(X4)
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_47,negated_conjecture,
( app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0
| app(app(cons(X1,nil),cons(X2,nil)),X3) != esk49_0
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_33,c_0_4]) ).
cnf(c_0_48,negated_conjecture,
app(app(cons(esk52_0,nil),cons(esk53_0,nil)),esk54_0) = esk49_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]),c_0_38])]),c_0_39]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk54_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_35]),c_0_36]),c_0_37]),c_0_38])]),c_0_41]) ).
cnf(c_0_50,negated_conjecture,
ssItem(esk53_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35]),c_0_36]),c_0_37]),c_0_38])]),c_0_43]) ).
cnf(c_0_51,negated_conjecture,
ssItem(esk52_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_36]),c_0_37]),c_0_38])]),c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( app(app(cons(X1,nil),X2),cons(X3,nil)) = esk48_0
| app(app(cons(X3,nil),X2),cons(X1,nil)) != esk49_0
| app(app(cons(X4,nil),cons(X5,nil)),X6) != esk49_0
| ~ ssList(X6)
| ~ ssList(X2)
| ~ ssItem(X5)
| ~ ssItem(X4)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_9]),c_0_4]),c_0_4]) ).
cnf(c_0_53,negated_conjecture,
app(app(cons(esk59_0,nil),esk60_0),cons(esk58_0,nil)) != esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_54,negated_conjecture,
( app(app(cons(X1,nil),cons(X2,nil)),X3) != esk49_0
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_35]),c_0_36]),c_0_37]),c_0_38])]),c_0_53]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_48]),c_0_49]),c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC412+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 : n002.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
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:49:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.54/4.56 % Version : CSE_E---1.7
% 6.54/4.56 % Problem : theBenchmark.p
% 6.54/4.56 % SZS status Theorem for theBenchmark.p
% 6.54/4.56 % SZS output start CNFRefutation
% See solution above
% 6.54/4.58 % Total time : 3.373s
%------------------------------------------------------------------------------