%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET900+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n005.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 05:08:55 PM UTC 2026
% Result : Theorem 0.25s 1.62s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 24
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 101 ( 62 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 61 ~; 40 |; 12 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 18 !; 3 ?)
% 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(t41_zfmisc_1,conjecture,
! [X1,X2] :
~ ( X1 != singleton(X2)
& X1 != empty_set
& ! [X3] :
~ ( in(X3,X1)
& X3 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(l45_zfmisc_1,axiom,
! [X1,X2] :
~ ( X1 != singleton(X2)
& X1 != empty_set
& ! [X3] :
~ ( in(X3,X1)
& X3 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_zfmisc_1) ).
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_6,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_7,negated_conjecture,
~ ! [X1,X2] :
~ ( X1 != singleton(X2)
& X1 != empty_set
& ! [X3] :
~ ( in(X3,X1)
& X3 != X2 ) ),
inference(assume_negation,[status(cth)],[t41_zfmisc_1]) ).
fof(i_0_8,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_9,plain,
! [X21,X22] :
( ( in(esk5_2(X21,X22),X21)
| X21 = singleton(X22)
| X21 = empty_set )
& ( esk5_2(X21,X22) != X22
| X21 = singleton(X22)
| X21 = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_zfmisc_1])])])]) ).
fof(i_0_10,plain,
! [X14,X15] :
( ~ in(X14,X15)
| ~ in(X15,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6])]) ).
fof(i_0_11,negated_conjecture,
! [X20] :
( esk3_0 != singleton(esk4_0)
& esk3_0 != empty_set
& ( ~ in(X20,esk3_0)
| X20 = esk4_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])])])]) ).
fof(i_0_12,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_8])]) ).
fof(i_0_13,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_14,plain,
( in(esk5_2(X1,X2),X1)
| X1 = singleton(X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_15,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_16,plain,
( X1 = singleton(X2)
| X1 = empty_set
| esk5_2(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_17,negated_conjecture,
( X1 = esk4_0
| ~ in(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_18,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_19,negated_conjecture,
esk3_0 != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_20,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_21,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_22,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_23,axiom,
X1 = X1 ).
cnf(i_0_24,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_25,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_26,axiom,
( X1 != X2
| esk5_2(X1,X3) = esk5_2(X2,X3) ) ).
cnf(i_0_27,axiom,
( X1 != X2
| esk5_2(X3,X1) = esk5_2(X3,X2) ) ).
cnf(i_0_28,axiom,
( X1 != X2
| singleton(X1) = singleton(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_31,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_23_001,axiom,
X1 = X1 ).
cnf(i_0_24_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_25_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_26_004,axiom,
( X1 != X2
| esk5_2(X1,X3) = esk5_2(X2,X3) ) ).
cnf(i_0_27_005,axiom,
( X1 != X2
| esk5_2(X3,X1) = esk5_2(X3,X2) ) ).
cnf(i_0_28_006,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_29_007,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_30_008,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_31_009,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_32,plain,
esk5_2(esk3_0,esk4_0) != esk4_0,
inference(scs_inference,[],[i_0_19,i_0_22,i_0_16]) ).
cnf(i_0_33,plain,
( X1 = empty_set
| esk5_2(X1,X2) != X2
| X1 = singleton(X2) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_34,plain,
in(esk5_2(esk3_0,esk4_0),esk3_0),
inference(scs_inference,[],[i_0_19,i_0_22,i_0_16,i_0_14]) ).
cnf(i_0_35,plain,
( X1 = singleton(X2)
| X1 = empty_set
| in(esk5_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_36,plain,
esk1_0 != esk2_0,
inference(scs_inference,[],[i_0_19,i_0_22,i_0_18,i_0_20,i_0_16,i_0_14,i_0_31]) ).
cnf(i_0_37,plain,
$false,
inference(scs_inference,[],[i_0_19,i_0_22,i_0_18,i_0_20,i_0_16,i_0_14,i_0_31,i_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET900+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.33 % Computer : n005.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 02:56:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.25/1.62 % Version : CSE_E---1.7
% 0.25/1.62 % Problem : theBenchmark.p
% 0.25/1.62 % SZS status Theorem for theBenchmark.p
% 0.25/1.62 % SZS output start CNFRefutation
% See solution above
% 0.25/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------