%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC200+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 : n022.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 05:18:42 PM UTC 2026
% Result : Theorem 1.41s 1.76s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 129 ( 27 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 158 ( 63 ~; 59 |; 16 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
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(c_0_6,plain,
! [X334,X335] :
( ~ ssList(X334)
| ~ ssItem(X335)
| hd(cons(X335,X334)) = X335 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_7,plain,
! [X226,X228] :
( ( ssItem(esk5_1(X226))
| ~ singletonP(X226)
| ~ ssList(X226) )
& ( cons(esk5_1(X226),nil) = X226
| ~ singletonP(X226)
| ~ ssList(X226) )
& ( ~ ssItem(X228)
| cons(X228,nil) != X226
| singletonP(X226)
| ~ ssList(X226) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_9,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_12,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
! [X464] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& singletonP(esk50_0)
& ( ssItem(esk52_1(X464))
| ~ ssItem(X464) )
& ( memberP(esk48_0,esk52_1(X464))
| ~ ssItem(X464) )
& ( X464 != esk52_1(X464)
| ~ ssItem(X464) ) ),
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_8])])])])]) ).
cnf(c_0_14,plain,
( esk5_1(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
singletonP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(c_0_18,plain,
! [X363,X364,X365] :
( ( ~ memberP(cons(X364,X365),X363)
| X363 = X364
| memberP(X365,X363)
| ~ ssList(X365)
| ~ ssItem(X364)
| ~ ssItem(X363) )
& ( X363 != X364
| memberP(cons(X364,X365),X363)
| ~ ssList(X365)
| ~ ssItem(X364)
| ~ ssItem(X363) )
& ( ~ memberP(X365,X363)
| memberP(cons(X364,X365),X363)
| ~ ssList(X365)
| ~ ssItem(X364)
| ~ ssItem(X363) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_19,plain,
( cons(hd(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
singletonP(esk48_0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( ssItem(hd(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
fof(c_0_23,plain,
! [X366] :
( ~ ssItem(X366)
| ~ memberP(nil,X366) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
cnf(c_0_24,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
cons(hd(esk48_0),nil) = esk48_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_26,negated_conjecture,
ssItem(hd(esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_21])]) ).
cnf(c_0_27,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( hd(esk48_0) = X1
| ~ memberP(esk48_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11]),c_0_26])]),c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( memberP(esk48_0,esk52_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( ssItem(esk52_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,negated_conjecture,
( X1 != esk52_1(X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_32,negated_conjecture,
( esk52_1(X1) = hd(esk48_0)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32])]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC200+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
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:32:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.41/1.76 % Version : CSE_E---1.7
% 1.41/1.76 % Problem : theBenchmark.p
% 1.41/1.76 % SZS status Theorem for theBenchmark.p
% 1.41/1.76 % SZS output start CNFRefutation
% See solution above
% 1.41/1.76 % Total time : 1.374s
%------------------------------------------------------------------------------