%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC366+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 : n016.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 05:19:22 PM UTC 2026
% Result : Theorem 1.36s 1.74s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 194 ( 51 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 247 ( 98 ~; 98 |; 31 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 30 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& app(X6,X3) = X5
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X4) = X7
& neq(nil,X4) ) ) )
| rearsegP(X2,X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& app(X6,X3) = X5
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X4) = X7
& neq(nil,X4) ) ) )
| rearsegP(X2,X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_8,negated_conjecture,
! [X466,X467,X468] :
( 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)
| ~ ssList(X466)
| esk51_0 = X466
| ~ ssList(X467)
| app(X467,esk50_0) != X466
| ~ ssItem(X468)
| cons(X468,nil) != X467
| hd(esk51_0) != X468
| ~ neq(nil,esk51_0) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X466)
| esk51_0 = X466
| ~ ssList(X467)
| app(X467,esk50_0) != X466
| ~ ssItem(X468)
| cons(X468,nil) != X467
| hd(esk51_0) != X468
| ~ neq(nil,esk51_0) )
& ( neq(esk49_0,nil)
| ~ rearsegP(esk49_0,esk48_0) )
& ( ~ neq(esk51_0,nil)
| ~ rearsegP(esk49_0,esk48_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_7])])])])]) ).
cnf(c_0_9,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_10,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_9]) ).
cnf(c_0_11,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( esk51_0 = X1
| ~ neq(esk51_0,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,esk50_0) != X1
| ~ ssItem(X3)
| cons(X3,nil) != X2
| hd(esk51_0) != X3
| ~ neq(nil,esk51_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_15,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| ssList(cons(X323,X322)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_16,negated_conjecture,
( app(cons(hd(esk51_0),nil),esk48_0) = esk51_0
| ~ ssList(app(cons(hd(esk51_0),nil),esk48_0))
| ~ ssList(cons(hd(esk51_0),nil))
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14])])])])]) ).
cnf(c_0_17,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_19,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssList(X342)
| ssList(app(X341,X342)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_20,negated_conjecture,
( app(cons(hd(esk51_0),nil),esk48_0) = esk51_0
| ~ ssList(app(cons(hd(esk51_0),nil),esk48_0))
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
( app(cons(hd(esk51_0),nil),esk48_0) = esk51_0
| ~ ssList(cons(hd(esk51_0),nil))
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
fof(c_0_24,plain,
! [X335] :
( ~ ssList(X335)
| nil = X335
| ssItem(hd(X335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_26,plain,
! [X235,X236,X238] :
( ( ssList(esk7_2(X235,X236))
| ~ rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( app(esk7_2(X235,X236),X236) = X235
| ~ rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ~ ssList(X238)
| app(X238,X236) != X235
| rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
cnf(c_0_27,negated_conjecture,
( app(cons(hd(esk51_0),nil),esk48_0) = esk51_0
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_18])]) ).
cnf(c_0_28,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_25,c_0_11]) ).
fof(c_0_30,plain,
! [X320,X321] :
( ( ~ neq(X320,X321)
| X320 != X321
| ~ ssList(X321)
| ~ ssList(X320) )
& ( X320 = X321
| neq(X320,X321)
| ~ ssList(X321)
| ~ ssList(X320) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_31,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( app(cons(hd(esk51_0),nil),esk48_0) = esk51_0
| esk51_0 = nil
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ rearsegP(esk49_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_35,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_21]) ).
cnf(c_0_36,negated_conjecture,
( app(cons(hd(esk51_0),nil),esk48_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29]),c_0_18])]) ).
cnf(c_0_37,negated_conjecture,
~ rearsegP(esk51_0,esk48_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_14]),c_0_11])]) ).
cnf(c_0_38,negated_conjecture,
( esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_22])]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_17]),c_0_18])]) ).
cnf(c_0_40,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_29])]) ).
cnf(c_0_42,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_43,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_14,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC366+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 : n016.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 04:47:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.36/1.74 % Version : CSE_E---1.7
% 1.36/1.74 % Problem : theBenchmark.p
% 1.36/1.74 % SZS status Theorem for theBenchmark.p
% 1.36/1.74 % SZS output start CNFRefutation
% See solution above
% 1.36/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------