%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC204+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 : n019.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 05:18:43 PM UTC 2026
% Result : Theorem 1.30s 1.72s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 14 unt; 0 def)
% Number of atoms : 181 ( 65 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 208 ( 78 ~; 84 |; 24 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 30 !; 4 ?)
% 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)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| neq(X1,nil) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(c_0_9,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)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| neq(X1,nil) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_10,negated_conjecture,
! [X464,X465] :
( 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(X464)
| esk51_0 = X464
| ~ ssList(X465)
| tl(esk51_0) != X465
| app(esk50_0,X465) != X464
| ~ neq(nil,esk51_0) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X464)
| esk51_0 = X464
| ~ ssList(X465)
| tl(esk51_0) != X465
| app(esk50_0,X465) != X464
| ~ neq(nil,esk51_0) )
& ( neq(esk49_0,nil)
| ~ neq(esk48_0,nil) )
& ( ~ neq(esk51_0,nil)
| ~ neq(esk48_0,nil) ) ),
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_9])])])])]) ).
cnf(c_0_11,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_12,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_11]) ).
cnf(c_0_13,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( esk51_0 = X1
| ~ neq(esk51_0,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| tl(esk51_0) != X2
| app(esk50_0,X2) != X1
| ~ neq(nil,esk51_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X336] :
( ~ ssList(X336)
| nil = X336
| ssList(tl(X336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( app(esk48_0,tl(esk51_0)) = esk51_0
| ~ ssList(app(esk48_0,tl(esk51_0)))
| ~ ssList(tl(esk51_0))
| ~ neq(nil,esk51_0) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16])])])]) ).
cnf(c_0_20,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_18,c_0_13]) ).
fof(c_0_22,plain,
! [X339,X340] :
( ~ ssList(X339)
| ~ ssList(X340)
| ssList(app(X339,X340)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_23,negated_conjecture,
( app(esk48_0,tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ ssList(app(esk48_0,tl(esk51_0)))
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ neq(esk48_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_27,plain,
! [X318,X319] :
( ( ~ neq(X318,X319)
| X318 != X319
| ~ ssList(X319)
| ~ ssList(X318) )
& ( X318 = X319
| neq(X318,X319)
| ~ ssList(X319)
| ~ ssList(X318) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_28,negated_conjecture,
( app(esk48_0,tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ ssList(tl(esk51_0))
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
~ neq(esk48_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_16])]) ).
cnf(c_0_30,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_32,negated_conjecture,
( app(esk48_0,tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_21])]) ).
cnf(c_0_33,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_25])]) ).
fof(c_0_34,plain,
! [X344] :
( ~ ssList(X344)
| app(nil,X344) = X344 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_35,negated_conjecture,
( app(nil,tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ neq(nil,esk51_0) ),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( app(nil,tl(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_21]),c_0_31])]) ).
fof(c_0_38,plain,
! [X422] :
( ~ ssList(X422)
| nil = X422
| cons(hd(X422),tl(X422)) = X422 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_39,negated_conjecture,
( tl(esk51_0) = esk51_0
| esk51_0 = nil
| ~ ssList(tl(esk51_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_40,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| cons(X323,X322) != X322 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_41,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( tl(esk51_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_20]),c_0_21])]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( cons(hd(esk51_0),esk51_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_21])]) ).
fof(c_0_45,plain,
! [X333] :
( ~ ssList(X333)
| nil = X333
| ssItem(hd(X333)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_46,negated_conjecture,
( esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_21])]) ).
cnf(c_0_47,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_48,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_21])]) ).
cnf(c_0_49,negated_conjecture,
~ neq(nil,nil),
inference(rw,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_48]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC204+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:34:44 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.30/1.72 % Version : CSE_E---1.7
% 1.30/1.72 % Problem : theBenchmark.p
% 1.30/1.72 % SZS status Theorem for theBenchmark.p
% 1.30/1.72 % SZS output start CNFRefutation
% See solution above
% 1.30/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------