%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET907+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 : n006.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 05:08:56 PM UTC 2026
% Result : Theorem 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 36
% Syntax : Number of formulae : 81 ( 32 unt; 0 def)
% Number of atoms : 152 ( 56 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 147 ( 76 ~; 54 |; 7 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 155 ( 10 sgn 48 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(t48_zfmisc_1,conjecture,
! [X1,X2,X3] :
( ( in(X1,X2)
& in(X3,X2) )
=> set_union2(unordered_pair(X1,X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_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(t38_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(t12_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_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_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_12,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_13,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_14,negated_conjecture,
~ ! [X1,X2,X3] :
( ( in(X1,X2)
& in(X3,X2) )
=> set_union2(unordered_pair(X1,X3),X2) = X2 ),
inference(assume_negation,[status(cth)],[t48_zfmisc_1]) ).
fof(i_0_15,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_16,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_17,plain,
! [X44,X45,X46] :
( ( in(X44,X46)
| ~ subset(unordered_pair(X44,X45),X46) )
& ( in(X45,X46)
| ~ subset(unordered_pair(X44,X45),X46) )
& ( ~ in(X44,X46)
| ~ in(X45,X46)
| subset(unordered_pair(X44,X45),X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(i_0_18,plain,
! [X34,X35] :
( empty(X34)
| ~ empty(set_union2(X34,X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])]) ).
fof(i_0_19,plain,
! [X36,X37] :
( empty(X36)
| ~ empty(set_union2(X37,X36)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])]) ).
fof(i_0_20,negated_conjecture,
( in(esk3_0,esk4_0)
& in(esk5_0,esk4_0)
& set_union2(unordered_pair(esk3_0,esk5_0),esk4_0) != esk4_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])])]) ).
fof(i_0_21,plain,
! [X28,X29] :
( ~ in(X28,X29)
| ~ in(X29,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])]) ).
fof(i_0_22,plain,
! [X42,X43] :
( ~ subset(X42,X43)
| set_union2(X42,X43) = X43 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(i_0_23,plain,
! [X32,X33] : set_union2(X32,X33) = set_union2(X33,X32),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_24,plain,
! [X30,X31] : unordered_pair(X30,X31) = unordered_pair(X31,X30),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_25,plain,
! [X38] : set_union2(X38,X38) = X38,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_26,plain,
! [X41] : subset(X41,X41),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_27,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_16])]) ).
fof(i_0_28,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_29,plain,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_30,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_32,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_33,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_34,negated_conjecture,
set_union2(unordered_pair(esk3_0,esk5_0),esk4_0) != esk4_0,
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_35,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_36,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_37,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_39,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_40,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_41,negated_conjecture,
in(esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_42,negated_conjecture,
in(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_43,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_44,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_45,axiom,
X1 = X1 ).
cnf(i_0_46,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_47,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_48,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_52,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_53,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_54,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_55,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_56,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_45_001,axiom,
X1 = X1 ).
cnf(i_0_46_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_47_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_48_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_49_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_50_006,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_51_007,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_52_008,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_53_009,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_54_010,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_55_011,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_56_012,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_57,plain,
~ subset(unordered_pair(esk3_0,esk5_0),esk4_0),
inference(scs_inference,[],[i_0_34,i_0_36]) ).
cnf(i_0_58,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_59,plain,
~ in(esk4_0,esk5_0),
inference(scs_inference,[],[i_0_34,i_0_41,i_0_36,i_0_35]) ).
cnf(i_0_60,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_61,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_34,i_0_41,i_0_39,i_0_36,i_0_35,i_0_46]) ).
cnf(i_0_62,plain,
in(X1,unordered_pair(X1,X2)),
inference(scs_inference,[],[i_0_34,i_0_41,i_0_40,i_0_39,i_0_36,i_0_35,i_0_46,i_0_30]) ).
cnf(i_0_63,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_64,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_65,plain,
in(X1,unordered_pair(X2,X1)),
inference(scs_inference,[],[i_0_34,i_0_41,i_0_40,i_0_63,i_0_39,i_0_36,i_0_35,i_0_46,i_0_30,i_0_31]) ).
cnf(i_0_66,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_67,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X2,X3) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_68,plain,
$false,
inference(scs_inference,[],[i_0_34,i_0_41,i_0_42,i_0_40,i_0_63,i_0_39,i_0_36,i_0_35,i_0_46,i_0_30,i_0_31,i_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET907+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 : n006.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 02:40:16 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Theorem for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.66 % Total time : 1.271s
%------------------------------------------------------------------------------