%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU122+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n022.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 05:10:40 PM UTC 2026
% Result : Theorem 0.23s 1.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 53)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t2_xboole_1,conjecture,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
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_10,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_11,negated_conjecture,
~ ! [X1] : subset(empty_set,X1),
inference(assume_negation,[status(cth)],[t2_xboole_1]) ).
fof(i_0_12,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_13,plain,
! [X21,X22,X23,X24,X25] :
( ( ~ subset(X21,X22)
| ~ in(X23,X21)
| in(X23,X22) )
& ( in(esk1_2(X24,X25),X24)
| subset(X24,X25) )
& ( ~ in(esk1_2(X24,X25),X25)
| subset(X24,X25) ) ),
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_tarski])])])])])]) ).
fof(i_0_14,plain,
! [X19,X20] :
( ~ in(X19,X20)
| ~ in(X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_10])]) ).
fof(i_0_15,plain,
! [X32,X33] :
( ~ in(X32,X33)
| ~ empty(X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_16,negated_conjecture,
~ subset(empty_set,esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_11])])]) ).
fof(i_0_17,plain,
! [X34,X35] :
( ~ empty(X34)
| X34 = X35
| ~ empty(X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_18,plain,
! [X29] : subset(X29,X29),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_19,plain,
! [X31] :
( ~ empty(X31)
| X31 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_20,plain,
~ empty(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_12])]) ).
fof(i_0_21,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_22,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_23,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_25,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_26,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_27,negated_conjecture,
~ subset(empty_set,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_28,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_29,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_30,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_31,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_32,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_33,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[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
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_41,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
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_38_005,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_39_006,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_40_007,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_41_008,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_42,plain,
~ in(X1,esk2_0),
inference(scs_inference,[],[i_0_32,i_0_26]) ).
cnf(i_0_43,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_44,plain,
esk4_0 != empty_set,
inference(scs_inference,[],[i_0_27,i_0_29,i_0_32,i_0_26,i_0_37]) ).
cnf(i_0_45,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_46,plain,
empty_set != esk4_0,
inference(scs_inference,[],[i_0_27,i_0_29,i_0_45,i_0_32,i_0_26,i_0_37,i_0_38]) ).
cnf(i_0_47,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_48,plain,
esk2_0 != esk3_0,
inference(scs_inference,[],[i_0_27,i_0_29,i_0_45,i_0_32,i_0_31,i_0_26,i_0_37,i_0_38,i_0_41]) ).
cnf(i_0_49,plain,
subset(esk2_0,X1),
inference(scs_inference,[],[i_0_27,i_0_29,i_0_45,i_0_32,i_0_31,i_0_26,i_0_37,i_0_38,i_0_41,i_0_24]) ).
cnf(i_0_50,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_51,plain,
~ empty(esk4_0),
inference(scs_inference,[],[i_0_27,i_0_29,i_0_45,i_0_32,i_0_31,i_0_26,i_0_37,i_0_38,i_0_41,i_0_24,i_0_30]) ).
cnf(i_0_52,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_53,plain,
( X1 != esk2_0
| ~ in(esk1_2(esk2_0,X2),X1) ),
inference(scs_inference,[],[i_0_27,i_0_29,i_0_45,i_0_32,i_0_31,i_0_26,i_0_37,i_0_38,i_0_41,i_0_24,i_0_30,i_0_40]) ).
cnf(i_0_54,plain,
( X1 != esk2_0
| X2 != esk1_2(esk2_0,X3)
| ~ in(X2,X1) ),
inference(scs_inference,[],[i_0_27,i_0_29,i_0_45,i_0_32,i_0_31,i_0_26,i_0_37,i_0_38,i_0_41,i_0_24,i_0_30,i_0_40,i_0_39]) ).
cnf(i_0_55,plain,
~ in(esk1_2(esk2_0,X1),esk2_0),
inference(equality_inference,[],[53]) ).
cnf(i_0_56,plain,
~ in(X1,empty_set),
inference(scs_inference,[],[i_0_33,i_0_26]) ).
cnf(i_0_57,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_58,plain,
esk2_0 != empty_set,
inference(scs_inference,[],[i_0_27,i_0_49,i_0_33,i_0_26,i_0_37]) ).
cnf(i_0_59,plain,
subset(esk2_0,X1),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_60,plain,
esk2_0 != esk4_0,
inference(scs_inference,[],[i_0_27,i_0_49,i_0_51,i_0_32,i_0_33,i_0_26,i_0_37,i_0_41]) ).
cnf(i_0_61,plain,
$false,
inference(scs_inference,[],[i_0_27,i_0_49,i_0_51,i_0_32,i_0_33,i_0_26,i_0_37,i_0_41,i_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU122+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:43:51 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 0.23/1.61 % Version : CSE_E---1.7
% 0.23/1.61 % Problem : theBenchmark.p
% 0.23/1.61 % SZS status Theorem for theBenchmark.p
% 0.23/1.61 % SZS output start CNFRefutation
% See solution above
% 0.23/1.67 % Total time : 1.273s
%------------------------------------------------------------------------------