%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET926+1 : TPTP v9.2.1. Released v3.2.0.
% 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 05:08:59 PM UTC 2026
% Result : Theorem 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 25
% Syntax : Number of formulae : 48 ( 15 unt; 0 def)
% Number of atoms : 93 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 49 ~; 37 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l34_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t69_zfmisc_1,conjecture,
! [X1,X2] :
( set_difference(singleton(X1),X2) = empty_set
| set_difference(singleton(X1),X2) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(l36_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = empty_set
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_7,plain,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[l34_zfmisc_1]) ).
fof(i_0_8,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_9,negated_conjecture,
~ ! [X1,X2] :
( set_difference(singleton(X1),X2) = empty_set
| set_difference(singleton(X1),X2) = singleton(X1) ),
inference(assume_negation,[status(cth)],[t69_zfmisc_1]) ).
fof(i_0_10,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_11,plain,
! [X15,X16] :
( ( set_difference(singleton(X15),X16) != singleton(X15)
| ~ in(X15,X16) )
& ( in(X15,X16)
| set_difference(singleton(X15),X16) = singleton(X15) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])]) ).
fof(i_0_12,plain,
! [X17,X18] :
( ( set_difference(singleton(X17),X18) != empty_set
| in(X17,X18) )
& ( ~ in(X17,X18)
| set_difference(singleton(X17),X18) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l36_zfmisc_1])]) ).
fof(i_0_13,plain,
! [X13,X14] :
( ~ in(X13,X14)
| ~ in(X14,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])]) ).
fof(i_0_14,negated_conjecture,
( set_difference(singleton(esk3_0),esk4_0) != empty_set
& set_difference(singleton(esk3_0),esk4_0) != singleton(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])])]) ).
fof(i_0_15,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_10])]) ).
fof(i_0_16,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_17,plain,
( set_difference(singleton(X1),X2) != singleton(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_18,plain,
( in(X1,X2)
| set_difference(singleton(X1),X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_19,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_20,plain,
( set_difference(singleton(X1),X2) = empty_set
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_21,plain,
( in(X1,X2)
| set_difference(singleton(X1),X2) = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_22,negated_conjecture,
set_difference(singleton(esk3_0),esk4_0) != singleton(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_23,negated_conjecture,
set_difference(singleton(esk3_0),esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_24,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_25,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_26,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_27,axiom,
X1 = X1 ).
cnf(i_0_28,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_29,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_30,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_31,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_32,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_33,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_34,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_27_001,axiom,
X1 = X1 ).
cnf(i_0_28_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_29_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_30_004,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_31_005,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_32_006,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_33_007,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_34_008,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_35_009,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_36,plain,
in(esk3_0,esk4_0),
inference(scs_inference,[],[i_0_22,i_0_21]) ).
cnf(i_0_37,plain,
( set_difference(singleton(X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_38,plain,
$false,
inference(scs_inference,[],[i_0_22,i_0_23,i_0_21,i_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET926+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n015.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 02:39:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Theorem for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.63 % Total time : 1.272s
%------------------------------------------------------------------------------