%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC310+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 : n023.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 05:19:08 PM UTC 2026
% Result : Theorem 1.36s 1.75s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 9 unt; 0 def)
% Number of atoms : 276 ( 115 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 349 ( 138 ~; 145 |; 41 &)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 44 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& X1 = X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X2) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X2) = X10
& neq(nil,X2) )
& neq(nil,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& X1 = X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X2) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X2) = X10
& neq(nil,X2) )
& neq(nil,X2) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_11,negated_conjecture,
! [X474,X475,X476,X477] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( nil = esk50_0
| nil != esk51_0 )
& ( ssItem(esk52_0)
| ~ neq(esk51_0,nil) )
& ( ssList(esk53_0)
| ~ neq(esk51_0,nil) )
& ( app(cons(esk52_0,nil),esk53_0) = esk51_0
| ~ neq(esk51_0,nil) )
& ( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssList(X474)
| esk48_0 != X474
| ~ ssList(X475)
| ~ ssList(X476)
| tl(esk49_0) != X475
| app(X475,X476) != X474
| ~ ssItem(X477)
| cons(X477,nil) != X476
| hd(esk49_0) != X477
| ~ neq(nil,esk49_0)
| ~ neq(nil,esk49_0)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssList(X474)
| esk48_0 != X474
| ~ ssList(X475)
| ~ ssList(X476)
| tl(esk49_0) != X475
| app(X475,X476) != X474
| ~ ssItem(X477)
| cons(X477,nil) != X476
| hd(esk49_0) != X477
| ~ neq(nil,esk49_0)
| ~ neq(nil,esk49_0)
| nil != 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_10])])])])]) ).
cnf(c_0_12,negated_conjecture,
( nil = esk49_0
| ~ ssList(X1)
| esk48_0 != X1
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk49_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk49_0) != X4
| ~ neq(nil,esk49_0)
| ~ neq(nil,esk49_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_13,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])])]) ).
cnf(c_0_14,negated_conjecture,
( esk49_0 = nil
| esk48_0 != X1
| hd(esk49_0) != X4
| tl(esk49_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk49_0) ),
inference(cn,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X344] :
( ~ ssList(X344)
| nil = X344
| ssList(tl(X344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_17,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( esk49_0 = nil
| app(tl(esk49_0),cons(hd(esk49_0),nil)) != esk48_0
| ~ ssList(cons(hd(esk49_0),nil))
| ~ ssList(tl(esk49_0))
| ~ neq(nil,esk49_0)
| ~ ssItem(hd(esk49_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])])])]),c_0_15]) ).
cnf(c_0_22,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_24,plain,
! [X328,X329] :
( ~ ssList(X328)
| ~ ssItem(X329)
| ssList(cons(X329,X328)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_25,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk49_0
| ~ neq(esk49_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( neq(esk49_0,nil)
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_27,plain,
! [X437,X438] :
( ~ ssList(X437)
| ~ ssItem(X438)
| cons(X438,X437) = app(cons(X438,nil),X437) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_28,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk49_0,nil) ),
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk49_0,nil) ),
inference(rw,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( esk49_0 = nil
| app(tl(esk49_0),cons(hd(esk49_0),nil)) != esk48_0
| ~ ssList(cons(hd(esk49_0),nil))
| ~ neq(nil,esk49_0)
| ~ ssItem(hd(esk49_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_31,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_33,plain,
! [X341] :
( ~ ssList(X341)
| nil = X341
| ssItem(hd(X341)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
fof(c_0_34,plain,
! [X342,X343] :
( ~ ssList(X342)
| ~ ssItem(X343)
| hd(cons(X343,X342)) = X343 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
cnf(c_0_35,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk49_0
| esk49_0 = nil ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( esk49_0 = nil
| ssItem(esk52_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_38,negated_conjecture,
( esk49_0 = nil
| ssList(esk53_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_39,negated_conjecture,
( esk49_0 = nil
| app(tl(esk49_0),cons(hd(esk49_0),nil)) != esk48_0
| ~ neq(nil,esk49_0)
| ~ ssItem(hd(esk49_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_40,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( cons(esk52_0,esk53_0) = esk49_0
| esk49_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).
fof(c_0_43,plain,
! [X345,X346] :
( ~ ssList(X345)
| ~ ssItem(X346)
| tl(cons(X346,X345)) = X345 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
cnf(c_0_44,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_45,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_46,negated_conjecture,
( esk49_0 = nil
| app(tl(esk49_0),cons(hd(esk49_0),nil)) != esk48_0
| ~ neq(nil,esk49_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23])]) ).
cnf(c_0_47,negated_conjecture,
( hd(esk49_0) = esk52_0
| esk49_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_37]),c_0_38]) ).
cnf(c_0_48,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk48_0
| ~ neq(esk49_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_18]) ).
cnf(c_0_50,negated_conjecture,
( esk49_0 = nil
| app(tl(esk49_0),cons(esk52_0,nil)) != esk48_0
| ~ neq(nil,esk49_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( tl(esk49_0) = esk53_0
| esk49_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_42]),c_0_37]),c_0_38]) ).
cnf(c_0_52,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk48_0
| esk49_0 = nil ),
inference(spm,[status(thm)],[c_0_49,c_0_26]) ).
fof(c_0_53,plain,
! [X326,X327] :
( ( ~ neq(X326,X327)
| X326 != X327
| ~ ssList(X327)
| ~ ssList(X326) )
& ( X326 = X327
| neq(X326,X327)
| ~ ssList(X327)
| ~ ssList(X326) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_54,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_55,negated_conjecture,
( esk49_0 = nil
| ~ neq(nil,esk49_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_56,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( esk48_0 = nil
| esk49_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_45]),c_0_18]) ).
cnf(c_0_58,negated_conjecture,
esk49_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_23]),c_0_32])]) ).
cnf(c_0_59,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_61,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_63,negated_conjecture,
neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_58]),c_0_61])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC310+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
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 04:44:08 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.36/1.75 % Version : CSE_E---1.7
% 1.36/1.75 % Problem : theBenchmark.p
% 1.36/1.75 % SZS status Theorem for theBenchmark.p
% 1.36/1.75 % SZS output start CNFRefutation
% See solution above
% 1.36/1.75 % Total time : 1.374s
%------------------------------------------------------------------------------