%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC219+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 05:18:46 PM UTC 2026
% Result : Theorem 2.50s 2.03s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 12 unt; 0 def)
% Number of atoms : 255 ( 77 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 332 ( 131 ~; 132 |; 38 &)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn 50 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X10,X9) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X10,X9) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_11,negated_conjecture,
! [X472,X473,X474,X477] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssItem(esk52_3(X472,X473,X474))
| ~ ssList(X474)
| app(app(X473,cons(X472,nil)),X474) != esk48_0
| ~ ssList(X473)
| ~ ssItem(X472) )
& ( memberP(X473,esk52_3(X472,X473,X474))
| ~ ssList(X474)
| app(app(X473,cons(X472,nil)),X474) != esk48_0
| ~ ssList(X473)
| ~ ssItem(X472) )
& ( memberP(X474,esk52_3(X472,X473,X474))
| ~ ssList(X474)
| app(app(X473,cons(X472,nil)),X474) != esk48_0
| ~ ssList(X473)
| ~ ssItem(X472) )
& ( leq(X472,esk52_3(X472,X473,X474))
| ~ ssList(X474)
| app(app(X473,cons(X472,nil)),X474) != esk48_0
| ~ ssList(X473)
| ~ ssItem(X472) )
& ( ~ leq(esk52_3(X472,X473,X474),X472)
| ~ ssList(X474)
| app(app(X473,cons(X472,nil)),X474) != esk48_0
| ~ ssList(X473)
| ~ ssItem(X472) )
& ( nil = esk51_0
| ssItem(esk53_0) )
& ( nil = esk50_0
| ssItem(esk53_0) )
& ( nil = esk51_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk53_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk53_0) )
& ( nil = esk51_0
| ~ ssItem(X477)
| esk53_0 = X477
| ~ memberP(esk51_0,X477)
| ~ leq(X477,esk53_0) )
& ( nil = esk50_0
| ~ ssItem(X477)
| esk53_0 = X477
| ~ memberP(esk51_0,X477)
| ~ leq(X477,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_10])])])])]) ).
fof(c_0_12,plain,
! [X349,X350,X351] :
( ~ ssList(X349)
| ~ ssList(X350)
| ~ ssItem(X351)
| cons(X351,app(X350,X349)) = app(cons(X351,X350),X349) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_13,negated_conjecture,
( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( nil = esk50_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
cons(esk53_0,nil) = esk48_0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_20,negated_conjecture,
ssItem(esk53_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_15]) ).
fof(c_0_21,plain,
! [X444] :
( ~ ssList(X444)
| app(X444,nil) = X444 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_22,plain,
! [X237,X238,X240] :
( ( ssList(esk6_2(X237,X238))
| ~ frontsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( app(X238,esk6_2(X237,X238)) = X237
| ~ frontsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ~ ssList(X240)
| app(X238,X240) != X237
| frontsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
fof(c_0_23,plain,
! [X347,X348] :
( ~ ssList(X347)
| ~ ssList(X348)
| ssList(app(X347,X348)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_24,plain,
! [X439,X440,X441] :
( ~ ssList(X439)
| ~ ssList(X440)
| ~ ssList(X441)
| app(app(X439,X440),X441) = app(X439,app(X440,X441)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
fof(c_0_25,plain,
! [X352] :
( ~ ssList(X352)
| app(nil,X352) = X352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_26,plain,
! [X434,X435,X436] :
( ~ ssList(X434)
| ~ ssList(X435)
| ~ ssList(X436)
| app(X435,X436) != app(X435,X434)
| X436 = X434 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
cnf(c_0_27,negated_conjecture,
( cons(esk53_0,app(nil,X1)) = app(esk48_0,X1)
| ~ ssList(X1) ),
inference(cn,[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])]) ).
cnf(c_0_28,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_32,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
app(esk48_0,nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_18]),c_0_19])]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_30]) ).
fof(c_0_38,plain,
! [X374] :
( ~ ssItem(X374)
| ~ memberP(nil,X374) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( memberP(X1,esk52_3(X2,X1,X3))
| ~ ssList(X3)
| app(app(X1,cons(X2,nil)),X3) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_40,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_19])]) ).
cnf(c_0_41,negated_conjecture,
( X1 = nil
| app(esk48_0,X1) != esk48_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19]),c_0_36])]) ).
cnf(c_0_42,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,negated_conjecture,
frontsegP(esk48_0,esk48_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_36]),c_0_19])]) ).
cnf(c_0_44,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( memberP(X1,esk52_3(esk53_0,X1,X2))
| app(app(X1,esk48_0),X2) != esk48_0
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_18]),c_0_20])]) ).
cnf(c_0_46,negated_conjecture,
app(nil,esk48_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_35]),c_0_19]),c_0_36])]) ).
cnf(c_0_47,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_48,negated_conjecture,
( esk6_2(esk48_0,esk48_0) = nil
| ~ ssList(esk6_2(esk48_0,esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_36])])]),c_0_43]),c_0_36])]) ).
cnf(c_0_49,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_50,negated_conjecture,
( app(esk48_0,X1) != esk48_0
| ~ ssList(X1)
| ~ ssItem(esk52_3(esk53_0,nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_19])]) ).
cnf(c_0_51,negated_conjecture,
( ssItem(esk52_3(X1,X2,esk6_2(esk48_0,app(X2,cons(X1,nil)))))
| ~ frontsegP(esk48_0,app(X2,cons(X1,nil)))
| ~ ssList(esk6_2(esk48_0,app(X2,cons(X1,nil))))
| ~ ssList(app(X2,cons(X1,nil)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_42])]),c_0_36])]) ).
cnf(c_0_52,negated_conjecture,
esk6_2(esk48_0,esk48_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_43]),c_0_36])]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_18]),c_0_46]),c_0_52]),c_0_35]),c_0_18]),c_0_46]),c_0_52]),c_0_19]),c_0_18]),c_0_46]),c_0_43]),c_0_18]),c_0_46]),c_0_36]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC219+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
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % 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 04:41:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.50/2.03 % Version : CSE_E---1.7
% 2.50/2.03 % Problem : theBenchmark.p
% 2.50/2.03 % SZS status Theorem for theBenchmark.p
% 2.50/2.03 % SZS output start CNFRefutation
% See solution above
% 2.50/2.04 % Total time : 1.372s
%------------------------------------------------------------------------------