%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET983+1 : TPTP v9.2.1. Released v3.2.0.
% 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 05:09:05 PM UTC 2026
% Result : Theorem 0.28s 1.61s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 25)
% Comments :
%------------------------------------------------------------------------------
fof(t137_zfmisc_1,conjecture,
! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X2,X3))
& in(X1,cartesian_product2(X4,X5)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t123_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X2,X3))
& in(X1,cartesian_product2(X4,X5)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
inference(assume_negation,[status(cth)],[t137_zfmisc_1]) ).
fof(i_0_9,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_10,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_11,plain,
! [X31,X32,X33,X34,X35,X36,X37,X38] :
( ( in(X34,X31)
| ~ in(X34,X33)
| X33 != set_intersection2(X31,X32) )
& ( in(X34,X32)
| ~ in(X34,X33)
| X33 != set_intersection2(X31,X32) )
& ( ~ in(X35,X31)
| ~ in(X35,X32)
| in(X35,X33)
| X33 != set_intersection2(X31,X32) )
& ( ~ in(esk1_3(X36,X37,X38),X38)
| ~ in(esk1_3(X36,X37,X38),X36)
| ~ in(esk1_3(X36,X37,X38),X37)
| X38 = set_intersection2(X36,X37) )
& ( in(esk1_3(X36,X37,X38),X36)
| in(esk1_3(X36,X37,X38),X38)
| X38 = set_intersection2(X36,X37) )
& ( in(esk1_3(X36,X37,X38),X37)
| in(esk1_3(X36,X37,X38),X38)
| X38 = set_intersection2(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)],[d3_xboole_0])])])])])]) ).
fof(i_0_12,negated_conjecture,
( in(esk4_0,cartesian_product2(esk5_0,esk6_0))
& in(esk4_0,cartesian_product2(esk7_0,esk8_0))
& ~ in(esk4_0,cartesian_product2(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk8_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])])]) ).
fof(i_0_13,plain,
! [X43,X44,X45,X46] : cartesian_product2(set_intersection2(X43,X44),set_intersection2(X45,X46)) = set_intersection2(cartesian_product2(X43,X45),cartesian_product2(X44,X46)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(i_0_14,plain,
! [X27,X28] :
( ~ in(X27,X28)
| ~ in(X28,X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])]) ).
fof(i_0_15,plain,
! [X29,X30] : set_intersection2(X29,X30) = set_intersection2(X30,X29),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_16,plain,
! [X40] : set_intersection2(X40,X40) = X40,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_17,plain,
~ empty(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_10])]) ).
fof(i_0_18,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_19,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk1_3(X1,X2,X3),X3)
| ~ in(esk1_3(X1,X2,X3),X1)
| ~ in(esk1_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_20,plain,
( in(esk1_3(X1,X2,X3),X1)
| in(esk1_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_21,plain,
( in(esk1_3(X1,X2,X3),X2)
| in(esk1_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_22,negated_conjecture,
~ in(esk4_0,cartesian_product2(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk8_0))),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_23,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_25,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_26,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_27,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_28,negated_conjecture,
in(esk4_0,cartesian_product2(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_29,negated_conjecture,
in(esk4_0,cartesian_product2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_30,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_31,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_32,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_33,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_34,axiom,
X1 = X1 ).
cnf(i_0_35,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_36,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_37,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_41,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_34_001,axiom,
X1 = X1 ).
cnf(i_0_35_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_36_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_37_004,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_38_005,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_39_006,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_40_007,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_41_008,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_42_009,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_43_010,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_44,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,X3) ),
inference(equality_inference,[],[24]) ).
cnf(i_0_45,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(equality_inference,[],[25]) ).
cnf(i_0_46,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(equality_inference,[],[26]) ).
cnf(i_0_47,plain,
~ in(cartesian_product2(esk7_0,esk8_0),esk4_0),
inference(scs_inference,[],[i_0_28,i_0_27]) ).
cnf(i_0_48,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_49,plain,
~ in(esk4_0,set_intersection2(cartesian_product2(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk8_0)),X1)),
inference(scs_inference,[],[i_0_22,i_0_28,i_0_27,i_0_45]) ).
cnf(i_0_50,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_51,plain,
~ in(esk4_0,set_intersection2(X1,cartesian_product2(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk8_0)))),
inference(scs_inference,[],[i_0_22,i_0_28,i_0_27,i_0_45,i_0_46]) ).
cnf(i_0_52,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_53,plain,
X1 = set_intersection2(X1,X1),
inference(scs_inference,[],[i_0_22,i_0_28,i_0_31,i_0_27,i_0_45,i_0_46,i_0_35]) ).
cnf(i_0_54,plain,
in(esk4_0,set_intersection2(cartesian_product2(esk7_0,esk8_0),cartesian_product2(esk7_0,esk8_0))),
inference(scs_inference,[],[i_0_22,i_0_28,i_0_31,i_0_27,i_0_45,i_0_46,i_0_35,i_0_44]) ).
cnf(i_0_55,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_56,plain,
~ in(set_intersection2(esk4_0,esk4_0),cartesian_product2(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk8_0))),
inference(scs_inference,[],[i_0_22,i_0_28,i_0_31,i_0_27,i_0_45,i_0_46,i_0_35,i_0_44,i_0_41]) ).
cnf(i_0_57,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_58,plain,
~ in(cartesian_product2(esk7_0,esk8_0),set_intersection2(esk4_0,esk4_0)),
inference(scs_inference,[],[i_0_22,i_0_28,i_0_31,i_0_57,i_0_27,i_0_45,i_0_46,i_0_35,i_0_44,i_0_41,i_0_42]) ).
cnf(i_0_59,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_60,plain,
esk2_0 != esk3_0,
inference(scs_inference,[],[i_0_22,i_0_28,i_0_31,i_0_57,i_0_33,i_0_32,i_0_27,i_0_45,i_0_46,i_0_35,i_0_44,i_0_41,i_0_42,i_0_43]) ).
cnf(i_0_61,plain,
$false,
inference(scs_inference,[],[i_0_22,i_0_28,i_0_29,i_0_31,i_0_57,i_0_23,i_0_33,i_0_32,i_0_27,i_0_45,i_0_46,i_0_35,i_0_44,i_0_41,i_0_42,i_0_43,i_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET983+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n007.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 02:40:39 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.28/1.61 % Version : CSE_E---1.7
% 0.28/1.61 % Problem : theBenchmark.p
% 0.28/1.61 % SZS status Theorem for theBenchmark.p
% 0.28/1.61 % SZS output start CNFRefutation
% See solution above
% 0.28/1.67 % Total time : 1.272s
%------------------------------------------------------------------------------