%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC025+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 : n004.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 05:17:57 PM UTC 2026
% Result : Theorem 1.42s 1.75s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 160 ( 57 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 186 ( 70 ~; 74 |; 22 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ duplicatefreeP(X3)
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X4,X5)
& memberP(X3,X5) )
| ( ~ memberP(X3,X5)
& memberP(X4,X5) ) ) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_6,plain,
! [X362,X363,X364] :
( ( ~ memberP(cons(X363,X364),X362)
| X362 = X363
| memberP(X364,X362)
| ~ ssList(X364)
| ~ ssItem(X363)
| ~ ssItem(X362) )
& ( X362 != X363
| memberP(cons(X363,X364),X362)
| ~ ssList(X364)
| ~ ssItem(X363)
| ~ ssItem(X362) )
& ( ~ memberP(X364,X362)
| memberP(cons(X363,X364),X362)
| ~ ssList(X364)
| ~ ssItem(X363)
| ~ ssItem(X362) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ duplicatefreeP(X3)
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X4,X5)
& memberP(X3,X5) )
| ( ~ memberP(X3,X5)
& memberP(X4,X5) ) ) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_8,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X421] :
( ~ ssList(X421)
| nil = X421
| cons(hd(X421),tl(X421)) = X421 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_10,plain,
! [X332] :
( ~ ssList(X332)
| nil = X332
| ssItem(hd(X332)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
fof(c_0_11,plain,
! [X335] :
( ~ ssList(X335)
| nil = X335
| ssList(tl(X335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_12,negated_conjecture,
! [X463] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& duplicatefreeP(esk50_0)
& ( memberP(esk51_0,X463)
| ~ memberP(esk50_0,X463)
| ~ ssItem(X463) )
& ( memberP(esk50_0,X463)
| ~ memberP(esk51_0,X463)
| ~ ssItem(X463) )
& ( nil = esk48_0
| nil = esk49_0 )
& ( nil != esk49_0
| nil = esk49_0 )
& ( nil = esk48_0
| nil != esk48_0 )
& ( 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_7])])])])]) ).
cnf(c_0_13,plain,
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( memberP(esk51_0,X1)
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( nil = X1
| memberP(X1,hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_23,negated_conjecture,
( esk50_0 = nil
| memberP(esk51_0,hd(esk50_0))
| ~ ssItem(hd(esk50_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,negated_conjecture,
( nil = esk48_0
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_26,plain,
! [X365] :
( ~ ssItem(X365)
| ~ memberP(nil,X365) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
( esk50_0 = nil
| memberP(esk51_0,hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_15]),c_0_21])]) ).
cnf(c_0_28,negated_conjecture,
( esk51_0 = nil
| esk50_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_18]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( esk50_0 = nil
| memberP(nil,hd(esk50_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( memberP(esk50_0,X1)
| ~ memberP(esk51_0,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0))
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_20]),c_0_33])]) ).
cnf(c_0_37,negated_conjecture,
( esk50_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_18]),c_0_25]) ).
cnf(c_0_38,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_15]),c_0_21])]) ).
cnf(c_0_39,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_15]),c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
esk51_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
memberP(nil,hd(esk51_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_38]),c_0_40]) ).
cnf(c_0_42,negated_conjecture,
~ ssItem(hd(esk51_0)),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_15]),c_0_33])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC025+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
% 0.14/0.32 % Computer : n004.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 04:15:32 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.42/1.75 % Version : CSE_E---1.7
% 1.42/1.75 % Problem : theBenchmark.p
% 1.42/1.75 % SZS status Theorem for theBenchmark.p
% 1.42/1.75 % SZS output start CNFRefutation
% See solution above
% 1.42/1.75 % Total time : 1.373s
%------------------------------------------------------------------------------