%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC311+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 : n015.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 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 9 unt; 0 def)
% Number of atoms : 247 ( 107 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 316 ( 122 ~; 127 |; 44 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Maximal term depth : 4 ( 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 : 72 ( 0 sgn 36 !; 12 ?)
% 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] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& tl(X4) = X6
& app(X6,X7) = X5
& ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X7
& hd(X4) = X8
& neq(nil,X4) )
& neq(nil,X4) ) ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X2
& app(X10,cons(X9,nil)) = X1 ) ) ) ) ) ) ) ) ),
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(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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ? [X5] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& tl(X4) = X6
& app(X6,X7) = X5
& ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X7
& hd(X4) = X8
& neq(nil,X4) )
& neq(nil,X4) ) ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X2
& app(X10,cons(X9,nil)) = X1 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_10,negated_conjecture,
! [X472,X473,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 )
& ( ~ ssList(X472)
| esk50_0 = X472
| ~ ssList(X473)
| ~ ssList(X474)
| tl(esk51_0) != X473
| app(X473,X474) != X472
| ~ ssItem(X475)
| cons(X475,nil) != X474
| hd(esk51_0) != X475
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0)
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssItem(X476)
| ~ ssList(X477)
| app(cons(X476,nil),X477) != esk49_0
| app(X477,cons(X476,nil)) != esk48_0
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssItem(X476)
| ~ ssList(X477)
| app(cons(X476,nil),X477) != esk49_0
| app(X477,cons(X476,nil)) != esk48_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_9])])])])]) ).
cnf(c_0_11,negated_conjecture,
( esk50_0 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk51_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk51_0) != X4
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_12,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_13,negated_conjecture,
( esk50_0 = X1
| hd(esk51_0) != X4
| tl(esk51_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk51_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X344] :
( ~ ssList(X344)
| nil = X344
| ssList(tl(X344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_18,negated_conjecture,
( 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)
| ~ neq(esk49_0,nil)
| ~ ssItem(hd(esk49_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_15]),c_0_15]),c_0_15])])])])]),c_0_16]) ).
cnf(c_0_19,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
( neq(esk49_0,nil)
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_22,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_23,negated_conjecture,
( app(tl(esk49_0),cons(hd(esk49_0),nil)) = esk48_0
| esk49_0 = nil
| ~ ssList(cons(hd(esk49_0),nil))
| ~ neq(nil,esk49_0)
| ~ ssItem(hd(esk49_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_24,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_26,plain,
! [X341] :
( ~ ssList(X341)
| nil = X341
| ssItem(hd(X341)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_27,negated_conjecture,
( app(tl(esk49_0),cons(hd(esk49_0),nil)) = esk48_0
| 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_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_29,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_30,negated_conjecture,
( app(tl(esk49_0),cons(hd(esk49_0),nil)) = esk48_0
| esk49_0 = nil
| ~ neq(nil,esk49_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20])]) ).
cnf(c_0_31,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( nil = esk49_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk49_0
| app(X2,cons(X1,nil)) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,negated_conjecture,
( app(tl(esk49_0),cons(hd(esk49_0),nil)) = esk48_0
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20]),c_0_25])]) ).
cnf(c_0_34,negated_conjecture,
( esk49_0 = nil
| app(cons(hd(esk49_0),nil),tl(esk49_0)) != esk49_0
| ~ ssList(tl(esk49_0))
| ~ ssItem(hd(esk49_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( esk49_0 = nil
| app(cons(hd(esk49_0),nil),tl(esk49_0)) != esk49_0
| ~ ssItem(hd(esk49_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_20])]) ).
fof(c_0_36,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_37,negated_conjecture,
( esk49_0 = nil
| app(cons(hd(esk49_0),nil),tl(esk49_0)) != esk49_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_20])]) ).
cnf(c_0_38,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( esk49_0 = nil
| cons(hd(esk49_0),tl(esk49_0)) != esk49_0
| ~ ssList(tl(esk49_0))
| ~ ssItem(hd(esk49_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( esk49_0 = nil
| cons(hd(esk49_0),tl(esk49_0)) != esk49_0
| ~ ssItem(hd(esk49_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_20])]) ).
fof(c_0_41,plain,
! [X430] :
( ~ ssList(X430)
| nil = X430
| cons(hd(X430),tl(X430)) = X430 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_42,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_43,negated_conjecture,
( esk49_0 = nil
| cons(hd(esk49_0),tl(esk49_0)) != esk49_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_20])]) ).
cnf(c_0_44,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( esk48_0 = nil
| esk49_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_14]),c_0_15]) ).
cnf(c_0_46,negated_conjecture,
esk49_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_20])]) ).
cnf(c_0_47,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_48,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_49,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_51,negated_conjecture,
neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_46]),c_0_49])]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC311+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
% 0.16/0.33 % Computer : n015.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 04:43:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------