%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC378+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 : n014.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 05:19:24 PM UTC 2026
% Result : Theorem 1.61s 1.80s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 135 ( 25 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 156 ( 60 ~; 63 |; 18 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != X4
| app(X6,X5) != X3 ) )
| ! [X7] :
( ~ ssItem(X7)
| ( ~ memberP(X2,X7)
& ~ memberP(X1,X7) )
| ( memberP(X2,X7)
& memberP(X1,X7) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != X4
| app(X6,X5) != X3 ) )
| ! [X7] :
( ~ ssItem(X7)
| ( ~ memberP(X2,X7)
& ~ memberP(X1,X7) )
| ( memberP(X2,X7)
& memberP(X1,X7) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_4,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& ssList(esk53_0)
& app(esk52_0,esk53_0) = esk51_0
& app(esk53_0,esk52_0) = esk50_0
& ssItem(esk54_0)
& ( memberP(esk49_0,esk54_0)
| memberP(esk48_0,esk54_0) )
& ( ~ memberP(esk49_0,esk54_0)
| ~ memberP(esk48_0,esk54_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X433,X434,X435] :
( ~ ssList(X433)
| ~ ssList(X434)
| ~ ssList(X435)
| app(app(X433,X434),X435) = app(X433,app(X434,X435)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_6,negated_conjecture,
app(esk53_0,esk52_0) = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,plain,
! [X362,X363,X364] :
( ( ~ memberP(app(X363,X364),X362)
| memberP(X363,X362)
| memberP(X364,X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) )
& ( ~ memberP(X363,X362)
| memberP(app(X363,X364),X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) )
& ( ~ memberP(X364,X362)
| memberP(app(X363,X364),X362)
| ~ ssList(X364)
| ~ ssList(X363)
| ~ ssItem(X362) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_9,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
app(esk53_0,esk52_0) = esk48_0,
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
app(esk52_0,esk53_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,plain,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
( memberP(esk49_0,esk54_0)
| memberP(esk48_0,esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,negated_conjecture,
ssItem(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,negated_conjecture,
( app(esk53_0,app(esk52_0,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_9,c_0_10]),c_0_11]),c_0_12])]) ).
cnf(c_0_20,negated_conjecture,
app(esk52_0,esk53_0) = esk49_0,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( memberP(app(X1,esk49_0),esk54_0)
| memberP(esk48_0,esk54_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_22,negated_conjecture,
app(esk53_0,esk49_0) = app(esk48_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_12])]) ).
cnf(c_0_23,plain,
( memberP(X1,X3)
| memberP(X2,X3)
| ~ memberP(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( memberP(app(esk48_0,esk53_0),esk54_0)
| memberP(esk48_0,esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_12])]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_26,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( memberP(esk48_0,esk54_0)
| memberP(esk53_0,esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_12]),c_0_25]),c_0_18])]) ).
cnf(c_0_28,negated_conjecture,
( memberP(app(esk53_0,X1),esk54_0)
| memberP(esk48_0,esk54_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_12]),c_0_18])]) ).
cnf(c_0_29,negated_conjecture,
memberP(esk48_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_10]),c_0_11])]) ).
cnf(c_0_30,negated_conjecture,
( app(esk52_0,app(esk53_0,X1)) = app(esk49_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_20]),c_0_12]),c_0_11])]) ).
cnf(c_0_31,negated_conjecture,
( memberP(app(X1,esk48_0),esk54_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_29]),c_0_25]),c_0_18])]) ).
cnf(c_0_32,negated_conjecture,
app(esk52_0,esk48_0) = app(esk49_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_10]),c_0_11])]) ).
cnf(c_0_33,negated_conjecture,
( ~ memberP(esk49_0,esk54_0)
| ~ memberP(esk48_0,esk54_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_34,negated_conjecture,
memberP(app(esk49_0,esk52_0),esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_11])]) ).
cnf(c_0_35,negated_conjecture,
~ memberP(esk49_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_29])]) ).
cnf(c_0_36,negated_conjecture,
memberP(esk52_0,esk54_0),
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_23,c_0_34]),c_0_11]),c_0_17]),c_0_18])]),c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( memberP(app(esk52_0,X1),esk54_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_11]),c_0_18])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_12])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC378+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:47:06 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.61/1.80 % Version : CSE_E---1.7
% 1.61/1.80 % Problem : theBenchmark.p
% 1.61/1.80 % SZS status Theorem for theBenchmark.p
% 1.61/1.80 % SZS output start CNFRefutation
% See solution above
% 1.61/1.81 % Total time : 1.376s
%------------------------------------------------------------------------------