%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU151+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n011.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 05:10:48 PM UTC 2026
% Result : Theorem 0.29s 1.61s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 13)
% 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(t10_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
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_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(i_0_4,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
inference(assume_negation,[status(cth)],[t10_zfmisc_1]) ).
fof(i_0_6,plain,
! [X21,X22,X23,X24,X25,X26,X27,X28] :
( ( ~ in(X24,X23)
| X24 = X21
| X24 = X22
| X23 != unordered_pair(X21,X22) )
& ( X25 != X21
| in(X25,X23)
| X23 != unordered_pair(X21,X22) )
& ( X25 != X22
| in(X25,X23)
| X23 != unordered_pair(X21,X22) )
& ( esk1_3(X26,X27,X28) != X26
| ~ in(esk1_3(X26,X27,X28),X28)
| X28 = unordered_pair(X26,X27) )
& ( esk1_3(X26,X27,X28) != X27
| ~ in(esk1_3(X26,X27,X28),X28)
| X28 = unordered_pair(X26,X27) )
& ( in(esk1_3(X26,X27,X28),X28)
| esk1_3(X26,X27,X28) = X26
| esk1_3(X26,X27,X28) = X27
| X28 = unordered_pair(X26,X27) ) ),
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_7,plain,
! [X17,X18] :
( ~ in(X17,X18)
| ~ in(X18,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_4])]) ).
fof(i_0_8,plain,
! [X19,X20] : unordered_pair(X19,X20) = unordered_pair(X20,X19),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_9,negated_conjecture,
( unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk5_0)
& esk2_0 != esk4_0
& esk2_0 != esk5_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5])])]) ).
cnf(i_0_10,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_6]),
[final] ).
cnf(i_0_11,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_6]),
[final] ).
cnf(i_0_12,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_6]),
[final] ).
cnf(i_0_13,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_14,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_15,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_16,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_18,negated_conjecture,
unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_19,negated_conjecture,
esk2_0 != esk5_0,
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_20,negated_conjecture,
esk2_0 != esk4_0,
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_21,axiom,
X1 = X1 ).
cnf(i_0_22,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_23,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_24,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_25,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_26,axiom,
( X1 != X2
| esk1_3(X1,X3,X4) = esk1_3(X2,X3,X4) ) ).
cnf(i_0_27,axiom,
( X1 != X2
| esk1_3(X3,X1,X4) = esk1_3(X3,X2,X4) ) ).
cnf(i_0_28,axiom,
( X1 != X2
| esk1_3(X3,X4,X1) = esk1_3(X3,X4,X2) ) ).
cnf(i_0_29,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_30,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_21_001,axiom,
X1 = X1 ).
cnf(i_0_22_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_23_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_24_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_25_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_26_006,axiom,
( X1 != X2
| esk1_3(X1,X3,X4) = esk1_3(X2,X3,X4) ) ).
cnf(i_0_27_007,axiom,
( X1 != X2
| esk1_3(X3,X1,X4) = esk1_3(X3,X2,X4) ) ).
cnf(i_0_28_008,axiom,
( X1 != X2
| esk1_3(X3,X4,X1) = esk1_3(X3,X4,X2) ) ).
cnf(i_0_29_009,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_30_010,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_31,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[13]) ).
cnf(i_0_32,plain,
unordered_pair(esk4_0,esk5_0) = unordered_pair(esk2_0,esk3_0),
inference(scs_inference,[],[i_0_18,i_0_22]) ).
cnf(i_0_33,plain,
in(unordered_pair(esk2_0,esk3_0),unordered_pair(X1,unordered_pair(esk4_0,esk5_0))),
inference(scs_inference,[],[i_0_18,i_0_17,i_0_22,i_0_15]) ).
cnf(i_0_34,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_35,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_36,plain,
in(unordered_pair(esk2_0,esk3_0),unordered_pair(unordered_pair(esk4_0,esk5_0),X1)),
inference(scs_inference,[],[i_0_18,i_0_17,i_0_34,i_0_22,i_0_15,i_0_16]) ).
cnf(i_0_37,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_38,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_39,plain,
unordered_pair(esk3_0,esk2_0) = unordered_pair(esk4_0,esk5_0),
inference(scs_inference,[],[i_0_18,i_0_17,i_0_34,i_0_37,i_0_22,i_0_15,i_0_16,i_0_23]) ).
cnf(i_0_40,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_41,plain,
~ in(esk2_0,unordered_pair(esk2_0,esk3_0)),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_20,i_0_17,i_0_34,i_0_37,i_0_22,i_0_15,i_0_16,i_0_23,i_0_13]) ).
cnf(i_0_42,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_43,plain,
~ in(unordered_pair(X1,unordered_pair(esk4_0,esk5_0)),unordered_pair(esk2_0,esk3_0)),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_20,i_0_17,i_0_34,i_0_37,i_0_22,i_0_15,i_0_16,i_0_23,i_0_13,i_0_14]) ).
cnf(i_0_44,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_45,plain,
( X1 != esk2_0
| ~ in(X1,unordered_pair(esk2_0,esk3_0)) ),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_20,i_0_17,i_0_34,i_0_37,i_0_22,i_0_15,i_0_16,i_0_23,i_0_13,i_0_14,i_0_29]) ).
cnf(i_0_46,plain,
~ in(esk2_0,unordered_pair(esk3_0,esk2_0)),
inference(scs_inference,[],[i_0_18,i_0_19,i_0_20,i_0_17,i_0_34,i_0_37,i_0_40,i_0_22,i_0_15,i_0_16,i_0_23,i_0_13,i_0_14,i_0_29,i_0_30]) ).
cnf(i_0_47,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_48,plain,
~ in(esk2_0,unordered_pair(esk2_0,esk3_0)),
inference(equality_inference,[],[45]) ).
cnf(i_0_49,plain,
~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),X1),unordered_pair(esk2_0,esk3_0)),
inference(scs_inference,[],[i_0_36,i_0_14]) ).
cnf(i_0_50,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_51,plain,
unordered_pair(esk4_0,esk5_0) = unordered_pair(esk3_0,esk2_0),
inference(scs_inference,[],[i_0_36,i_0_39,i_0_14,i_0_22]) ).
cnf(i_0_52,plain,
esk2_0 != esk3_0,
inference(scs_inference,[],[i_0_41,i_0_36,i_0_39,i_0_17,i_0_14,i_0_22,i_0_15]) ).
cnf(i_0_53,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_54,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_56,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_57,plain,
~ in(esk2_0,unordered_pair(esk4_0,esk5_0)),
inference(scs_inference,[],[i_0_41,i_0_36,i_0_32,i_0_39,i_0_17,i_0_53,i_0_14,i_0_22,i_0_15,i_0_16,i_0_30]) ).
cnf(i_0_58,plain,
~ in(esk2_0,unordered_pair(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_19,i_0_41,i_0_36,i_0_32,i_0_39,i_0_17,i_0_53,i_0_56,i_0_14,i_0_22,i_0_15,i_0_16,i_0_30,i_0_13]) ).
cnf(i_0_59,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_60,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_61,plain,
( X1 != esk2_0
| ~ in(X1,unordered_pair(esk3_0,esk2_0)) ),
inference(scs_inference,[],[i_0_19,i_0_41,i_0_46,i_0_36,i_0_32,i_0_39,i_0_17,i_0_53,i_0_56,i_0_14,i_0_22,i_0_15,i_0_16,i_0_30,i_0_13,i_0_29]) ).
cnf(i_0_62,plain,
~ in(esk2_0,unordered_pair(esk3_0,esk2_0)),
inference(equality_inference,[],[61]) ).
cnf(i_0_65,plain,
~ in(unordered_pair(X1,unordered_pair(esk4_0,esk5_0)),unordered_pair(esk4_0,esk5_0)),
inference(scs_inference,[],[i_0_43,i_0_51,i_0_57,i_0_32,i_0_15,i_0_16,i_0_30]) ).
cnf(i_0_66,plain,
~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),X1),unordered_pair(esk4_0,esk5_0)),
inference(scs_inference,[],[i_0_43,i_0_51,i_0_57,i_0_32,i_0_17,i_0_15,i_0_16,i_0_30,i_0_29]) ).
cnf(i_0_67,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_68,plain,
~ in(esk2_0,unordered_pair(esk4_0,esk4_0)),
inference(scs_inference,[],[i_0_20,i_0_43,i_0_51,i_0_57,i_0_32,i_0_17,i_0_67,i_0_15,i_0_16,i_0_30,i_0_29,i_0_13]) ).
cnf(i_0_69,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_70,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_71,plain,
unordered_pair(X1,unordered_pair(esk4_0,esk5_0)) != esk2_0,
inference(scs_inference,[],[i_0_65,i_0_51,i_0_16]) ).
cnf(i_0_72,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_73,plain,
unordered_pair(X1,unordered_pair(esk4_0,esk5_0)) != esk3_0,
inference(scs_inference,[],[i_0_65,i_0_51,i_0_16,i_0_15]) ).
cnf(i_0_74,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_75,plain,
( X1 != esk2_0
| ~ in(X1,unordered_pair(esk5_0,esk5_0)) ),
inference(scs_inference,[],[i_0_58,i_0_65,i_0_51,i_0_16,i_0_15,i_0_29]) ).
cnf(i_0_76,plain,
~ in(esk2_0,unordered_pair(esk5_0,esk5_0)),
inference(equality_inference,[],[75]) ).
cnf(i_0_77,plain,
unordered_pair(unordered_pair(esk4_0,esk5_0),X1) != esk2_0,
inference(scs_inference,[],[i_0_51,i_0_66,i_0_16]) ).
cnf(i_0_78,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_79,plain,
unordered_pair(unordered_pair(esk4_0,esk5_0),X1) != esk3_0,
inference(scs_inference,[],[i_0_51,i_0_66,i_0_16,i_0_15]) ).
cnf(i_0_80,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_81,plain,
( X1 != esk2_0
| ~ in(X1,unordered_pair(esk4_0,esk4_0)) ),
inference(scs_inference,[],[i_0_68,i_0_51,i_0_66,i_0_16,i_0_15,i_0_29]) ).
cnf(i_0_82,plain,
~ in(esk2_0,unordered_pair(esk4_0,esk4_0)),
inference(equality_inference,[],[81]) ).
cnf(i_0_85,plain,
( X1 != esk2_0
| ~ in(X1,unordered_pair(esk4_0,esk5_0)) ),
inference(scs_inference,[],[i_0_51,i_0_32,i_0_57,i_0_16,i_0_15,i_0_29]) ).
cnf(i_0_86,plain,
~ in(esk2_0,unordered_pair(esk4_0,esk5_0)),
inference(equality_inference,[],[85]) ).
cnf(i_0_88,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_89,plain,
~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),X1),unordered_pair(esk3_0,esk2_0)),
inference(scs_inference,[],[i_0_41,i_0_17,i_0_88,i_0_49,i_0_16,i_0_30]) ).
cnf(i_0_90,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_91,plain,
~ in(unordered_pair(X1,unordered_pair(esk4_0,esk5_0)),unordered_pair(esk3_0,esk2_0)),
inference(scs_inference,[],[i_0_41,i_0_17,i_0_88,i_0_90,i_0_49,i_0_16,i_0_30,i_0_29]) ).
cnf(i_0_92,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_94,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_96,plain,
$false,
inference(scs_inference,[],[i_0_41,i_0_17,i_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU151+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:45:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.29/1.61 % Version : CSE_E---1.7
% 0.29/1.61 % Problem : theBenchmark.p
% 0.29/1.61 % SZS status Theorem for theBenchmark.p
% 0.29/1.61 % SZS output start CNFRefutation
% See solution above
% 0.40/1.73 % Total time : 1.270s
%------------------------------------------------------------------------------