%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET603+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n007.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 05:08:06 PM UTC 2026
% Result : Theorem 1.43s 1.78s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 12 unt; 0 def)
% Number of atoms : 99 ( 22 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 42 |; 9 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 4 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(member_equal,axiom,
! [X1,X2] :
( ! [X3] :
( member(X3,X1)
<=> member(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_equal) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_th74,conjecture,
! [X1] : difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th74) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X26,X27,X28] :
( ( member(X28,X26)
| ~ member(X28,difference(X26,X27)) )
& ( ~ member(X28,X27)
| ~ member(X28,difference(X26,X27)) )
& ( ~ member(X28,X26)
| member(X28,X27)
| member(X28,difference(X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X46,X47,X48] :
( ( ~ empty(X46)
| ~ member(X47,X46) )
& ( member(esk4_1(X48),X48)
| empty(X48) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_10,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
cnf(c_0_11,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(esk4_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X29] : ~ member(X29,empty_set),
inference(variable_rename,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X23,X24] :
( ( ~ member(esk1_2(X23,X24),X23)
| ~ member(esk1_2(X23,X24),X24)
| X23 = X24 )
& ( member(esk1_2(X23,X24),X23)
| member(esk1_2(X23,X24),X24)
| X23 = X24 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_equal])])])]) ).
cnf(c_0_15,plain,
( empty(difference(X1,X2))
| ~ member(esk4_1(difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_18,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( ~ member(X34,X32)
| member(X34,X33)
| X32 != X33 )
& ( ~ member(X35,X33)
| member(X35,X32)
| X32 != X33 )
& ( ~ member(esk2_2(X36,X37),X36)
| ~ member(esk2_2(X36,X37),X37)
| X36 = X37 )
& ( member(esk2_2(X36,X37),X36)
| member(esk2_2(X36,X37),X37)
| X36 = X37 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_member_defn])])])])])]) ).
cnf(c_0_19,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( member(esk1_2(X1,X2),X1)
| member(esk1_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( empty(difference(X1,difference(X2,X3)))
| member(esk4_1(difference(X1,difference(X2,X3))),X3)
| ~ member(esk4_1(difference(X1,difference(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( empty(difference(X1,X2))
| member(esk4_1(difference(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_23,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,plain,
( empty_set = X1
| member(esk1_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( empty(difference(X1,difference(X1,X2)))
| member(esk4_1(difference(X1,difference(X1,X2))),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( difference(X1,X2) = X3
| member(esk2_2(difference(X1,X2),X3),X3)
| member(esk2_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_28,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
empty(difference(X1,difference(X1,empty_set))),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
fof(c_0_30,negated_conjecture,
~ ! [X1] : difference(X1,empty_set) = X1,
inference(assume_negation,[status(cth)],[prove_th74]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,plain,
( difference(X1,X2) = X1
| member(esk2_2(difference(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
difference(X1,difference(X1,empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_34,negated_conjecture,
difference(esk5_0,empty_set) != esk5_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_35,plain,
( difference(X1,X2) = X1
| ~ member(esk2_2(difference(X1,X2),X1),difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( member(X1,difference(X2,empty_set))
| ~ member(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_33]),c_0_19]) ).
cnf(c_0_37,negated_conjecture,
difference(esk5_0,empty_set) != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
difference(X1,empty_set) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_32]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET603+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n007.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 02:28:24 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.43/1.78 % Version : CSE_E---1.7
% 1.43/1.78 % Problem : theBenchmark.p
% 1.43/1.78 % SZS status Theorem for theBenchmark.p
% 1.43/1.78 % SZS output start CNFRefutation
% See solution above
% 1.43/1.78 % Total time : 1.373s
%------------------------------------------------------------------------------