%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET920+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 : n026.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 05:08:58 PM UTC 2026
% Result : Theorem 0.26s 1.61s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 27)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t63_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
=> in(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_zfmisc_1) ).
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(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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_9,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
=> in(X1,X3) ),
inference(assume_negation,[status(cth)],[t63_zfmisc_1]) ).
fof(i_0_11,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_12,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( in(X44,X41)
| ~ in(X44,X43)
| X43 != set_intersection2(X41,X42) )
& ( in(X44,X42)
| ~ in(X44,X43)
| X43 != set_intersection2(X41,X42) )
& ( ~ in(X45,X41)
| ~ in(X45,X42)
| in(X45,X43)
| X43 != set_intersection2(X41,X42) )
& ( ~ in(esk2_3(X46,X47,X48),X48)
| ~ in(esk2_3(X46,X47,X48),X46)
| ~ in(esk2_3(X46,X47,X48),X47)
| X48 = set_intersection2(X46,X47) )
& ( in(esk2_3(X46,X47,X48),X46)
| in(esk2_3(X46,X47,X48),X48)
| X48 = set_intersection2(X46,X47) )
& ( in(esk2_3(X46,X47,X48),X47)
| in(esk2_3(X46,X47,X48),X48)
| X48 = set_intersection2(X46,X47) ) ),
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_13,plain,
! [X32,X33,X34,X35,X36,X37,X38,X39] :
( ( ~ in(X35,X34)
| X35 = X32
| X35 = X33
| X34 != unordered_pair(X32,X33) )
& ( X36 != X32
| in(X36,X34)
| X34 != unordered_pair(X32,X33) )
& ( X36 != X33
| in(X36,X34)
| X34 != unordered_pair(X32,X33) )
& ( esk1_3(X37,X38,X39) != X37
| ~ in(esk1_3(X37,X38,X39),X39)
| X39 = unordered_pair(X37,X38) )
& ( esk1_3(X37,X38,X39) != X38
| ~ in(esk1_3(X37,X38,X39),X39)
| X39 = unordered_pair(X37,X38) )
& ( in(esk1_3(X37,X38,X39),X39)
| esk1_3(X37,X38,X39) = X37
| esk1_3(X37,X38,X39) = X38
| X39 = unordered_pair(X37,X38) ) ),
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)],[d2_tarski])])])])])]) ).
fof(i_0_14,plain,
! [X26,X27] :
( ~ in(X26,X27)
| ~ in(X27,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])]) ).
fof(i_0_15,negated_conjecture,
( set_intersection2(unordered_pair(esk5_0,esk6_0),esk7_0) = unordered_pair(esk5_0,esk6_0)
& ~ in(esk5_0,esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_10])])]) ).
fof(i_0_16,plain,
! [X30,X31] : set_intersection2(X30,X31) = set_intersection2(X31,X30),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_17,plain,
! [X28,X29] : unordered_pair(X28,X29) = unordered_pair(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_18,plain,
! [X50] : set_intersection2(X50,X50) = X50,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_19,plain,
~ empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_11])]) ).
fof(i_0_20,plain,
empty(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_21,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X3)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_22,plain,
( X3 = unordered_pair(X1,X2)
| esk1_3(X1,X2,X3) != X1
| ~ in(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_23,plain,
( X3 = unordered_pair(X1,X2)
| esk1_3(X1,X2,X3) != X2
| ~ in(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,plain,
( in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_25,plain,
( in(esk2_3(X1,X2,X3),X2)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_26,plain,
( in(esk1_3(X1,X2,X3),X3)
| esk1_3(X1,X2,X3) = X1
| esk1_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_27,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_28,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_29,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_30,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_31,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_32,negated_conjecture,
set_intersection2(unordered_pair(esk5_0,esk6_0),esk7_0) = unordered_pair(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_33,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_34,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_35,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_36,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_37,negated_conjecture,
~ in(esk5_0,esk7_0),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_38,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_39,plain,
~ empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_40,plain,
empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_41,axiom,
X1 = X1 ).
cnf(i_0_42,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_43,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_44,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| esk1_3(X1,X3,X4) = esk1_3(X2,X3,X4) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| esk1_3(X3,X1,X4) = esk1_3(X3,X2,X4) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| esk1_3(X3,X4,X1) = esk1_3(X3,X4,X2) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_52,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_53,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_41_001,axiom,
X1 = X1 ).
cnf(i_0_42_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_43_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_44_004,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_45_005,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_46_006,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_47_007,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_48_008,axiom,
( X1 != X2
| esk1_3(X1,X3,X4) = esk1_3(X2,X3,X4) ) ).
cnf(i_0_49_009,axiom,
( X1 != X2
| esk1_3(X3,X1,X4) = esk1_3(X3,X2,X4) ) ).
cnf(i_0_50_010,axiom,
( X1 != X2
| esk1_3(X3,X4,X1) = esk1_3(X3,X4,X2) ) ).
cnf(i_0_51_011,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_52_012,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_53_013,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_54,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,X3) ),
inference(equality_inference,[],[27]) ).
cnf(i_0_55,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(equality_inference,[],[28]) ).
cnf(i_0_56,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(equality_inference,[],[29]) ).
cnf(i_0_57,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[30]) ).
cnf(i_0_58,plain,
~ in(esk5_0,set_intersection2(esk7_0,X1)),
inference(scs_inference,[],[i_0_37,i_0_55]) ).
cnf(i_0_59,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_60,plain,
~ in(esk5_0,set_intersection2(X1,esk7_0)),
inference(scs_inference,[],[i_0_37,i_0_55,i_0_56]) ).
cnf(i_0_61,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_62,plain,
unordered_pair(esk5_0,esk6_0) = set_intersection2(unordered_pair(esk5_0,esk6_0),esk7_0),
inference(scs_inference,[],[i_0_32,i_0_37,i_0_55,i_0_56,i_0_42]) ).
cnf(i_0_64,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_65,plain,
esk5_0 != esk6_0,
inference(scs_inference,[],[i_0_32,i_0_37,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34]) ).
cnf(i_0_66,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_67,plain,
esk5_0 != set_intersection2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43]) ).
cnf(i_0_68,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_69,plain,
~ in(set_intersection2(esk5_0,esk5_0),esk7_0),
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_68,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43,i_0_51]) ).
cnf(i_0_70,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_71,plain,
~ in(esk5_0,set_intersection2(set_intersection2(esk7_0,X1),set_intersection2(esk7_0,X1))),
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_68,i_0_70,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43,i_0_51,i_0_52]) ).
cnf(i_0_72,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_73,plain,
esk3_0 != esk4_0,
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_68,i_0_70,i_0_39,i_0_40,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43,i_0_51,i_0_52,i_0_53]) ).
cnf(i_0_74,plain,
in(esk2_3(esk5_0,esk5_0,esk5_0),esk5_0),
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_68,i_0_70,i_0_39,i_0_40,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43,i_0_51,i_0_52,i_0_53,i_0_24]) ).
cnf(i_0_75,plain,
( X1 = set_intersection2(X2,X3)
| in(esk2_3(X2,X3,X1),X2)
| in(esk2_3(X2,X3,X1),X1) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_76,plain,
~ in(esk5_0,set_intersection2(set_intersection2(X1,esk7_0),set_intersection2(X1,esk7_0))),
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_68,i_0_70,i_0_72,i_0_39,i_0_40,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43,i_0_51,i_0_52,i_0_53,i_0_24,i_0_29]) ).
cnf(i_0_77,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_78,plain,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_79,plain,
~ in(esk5_0,set_intersection2(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk5_0))),
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_68,i_0_70,i_0_72,i_0_77,i_0_39,i_0_40,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43,i_0_51,i_0_52,i_0_53,i_0_24,i_0_29,i_0_30]) ).
cnf(i_0_80,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_81,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_82,plain,
$false,
inference(scs_inference,[],[i_0_32,i_0_37,i_0_38,i_0_68,i_0_70,i_0_72,i_0_77,i_0_39,i_0_40,i_0_55,i_0_56,i_0_42,i_0_33,i_0_34,i_0_43,i_0_51,i_0_52,i_0_53,i_0_24,i_0_29,i_0_30,i_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET920+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
% 0.15/0.33 % Computer : n026.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 02:39:38 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.26/1.61 % Version : CSE_E---1.7
% 0.26/1.61 % Problem : theBenchmark.p
% 0.26/1.61 % SZS status Theorem for theBenchmark.p
% 0.26/1.61 % SZS output start CNFRefutation
% See solution above
% 0.36/1.71 % Total time : 1.271s
%------------------------------------------------------------------------------