%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC324+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 : 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 05:19:11 PM UTC 2026
% Result : Theorem 1.66s 1.81s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 159 ( 74 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 198 ( 80 ~; 75 |; 29 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 26 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(X5,X6) = X2
& app(X6,X5) = X1 ) )
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) != X3
& app(cons(X7,nil),X8) = X4 ) )
| ( nil != X3
& nil = X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(X5,X6) = X2
& app(X6,X5) = X1 ) )
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) != X3
& app(cons(X7,nil),X8) = X4 ) )
| ( nil != X3
& nil = X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_7,negated_conjecture,
! [X468,X469,X470,X471] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssList(X468)
| ~ ssList(X469)
| app(X468,X469) != esk49_0
| app(X469,X468) != esk48_0 )
& ( ~ ssItem(X470)
| ~ ssList(X471)
| app(X471,cons(X470,nil)) = esk50_0
| app(cons(X470,nil),X471) != esk51_0 )
& ( nil = esk50_0
| nil != esk51_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,plain,
! [X438,X439] :
( ( nil = X439
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil = X438
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil != X439
| nil != X438
| nil = app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_9,plain,
! [X433,X434] :
( ~ ssList(X433)
| ~ ssItem(X434)
| cons(X434,X433) = app(cons(X434,nil),X433) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_10,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != esk49_0
| app(X2,X1) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_15,negated_conjecture,
( app(X2,cons(X1,nil)) = esk50_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_17,plain,
! [X332] :
( ( ssList(esk44_1(X332))
| nil = X332
| ~ ssList(X332) )
& ( ssItem(esk45_1(X332))
| nil = X332
| ~ ssList(X332) )
& ( cons(esk45_1(X332),esk44_1(X332)) = X332
| nil = X332
| ~ ssList(X332) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( app(X1,X2) != esk50_0
| app(X2,X1) != esk51_0
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_20,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]),c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
( app(X1,cons(X2,nil)) = esk50_0
| cons(X2,X1) != esk51_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_25,negated_conjecture,
esk51_0 != nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20]),c_0_14])]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( app(esk44_1(esk51_0),cons(esk45_1(esk51_0),nil)) = esk50_0
| ~ ssList(esk44_1(esk51_0))
| ~ ssItem(esk45_1(esk51_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23])]),c_0_24])]),c_0_25]) ).
cnf(c_0_27,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( app(esk44_1(esk51_0),cons(esk45_1(esk51_0),nil)) = esk50_0
| ~ ssItem(esk45_1(esk51_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24])]),c_0_25]) ).
cnf(c_0_29,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
app(esk44_1(esk51_0),cons(esk45_1(esk51_0),nil)) = esk50_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24])]),c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( app(cons(esk45_1(esk51_0),nil),esk44_1(esk51_0)) != esk51_0
| ~ ssList(cons(esk45_1(esk51_0),nil))
| ~ ssList(esk44_1(esk51_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
fof(c_0_32,plain,
! [X324,X325] :
( ~ ssList(X324)
| ~ ssItem(X325)
| ssList(cons(X325,X324)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_33,negated_conjecture,
( app(cons(esk45_1(esk51_0),nil),esk44_1(esk51_0)) != esk51_0
| ~ ssList(cons(esk45_1(esk51_0),nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_24])]),c_0_25]) ).
cnf(c_0_34,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( app(cons(esk45_1(esk51_0),nil),esk44_1(esk51_0)) != esk51_0
| ~ ssItem(esk45_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_14])]) ).
cnf(c_0_36,negated_conjecture,
app(cons(esk45_1(esk51_0),nil),esk44_1(esk51_0)) != esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_24])]),c_0_25]) ).
cnf(c_0_37,negated_conjecture,
( cons(esk45_1(esk51_0),esk44_1(esk51_0)) != esk51_0
| ~ ssList(esk44_1(esk51_0))
| ~ ssItem(esk45_1(esk51_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_38,negated_conjecture,
( cons(esk45_1(esk51_0),esk44_1(esk51_0)) != esk51_0
| ~ ssItem(esk45_1(esk51_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_24])]),c_0_25]) ).
cnf(c_0_39,negated_conjecture,
cons(esk45_1(esk51_0),esk44_1(esk51_0)) != esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_24])]),c_0_25]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_24])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC324+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 : n004.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 04:45:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.66/1.81 % Version : CSE_E---1.7
% 1.66/1.81 % Problem : theBenchmark.p
% 1.66/1.81 % SZS status Theorem for theBenchmark.p
% 1.66/1.81 % SZS output start CNFRefutation
% See solution above
% 1.66/1.82 % Total time : 1.374s
%------------------------------------------------------------------------------