%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET911+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 : n009.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 05:08:57 PM UTC 2026
% Result : Theorem 0.25s 1.62s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 25
% Syntax : Number of formulae : 44 ( 18 unt; 0 def)
% Number of atoms : 78 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 39 ~; 28 |; 1 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 1 sgn 21 !; 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(t52_zfmisc_1,conjecture,
! [X1,X2] :
( in(X1,X2)
=> set_intersection2(X2,singleton(X1)) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(l32_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> set_intersection2(X2,singleton(X1)) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_7,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_8,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> set_intersection2(X2,singleton(X1)) = singleton(X1) ),
inference(assume_negation,[status(cth)],[t52_zfmisc_1]) ).
fof(i_0_9,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_10,plain,
! [X24,X25] :
( ~ in(X24,X25)
| set_intersection2(X25,singleton(X24)) = singleton(X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_zfmisc_1])]) ).
fof(i_0_11,plain,
! [X18,X19] :
( ~ in(X18,X19)
| ~ in(X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])]) ).
fof(i_0_12,negated_conjecture,
( in(esk3_0,esk4_0)
& set_intersection2(esk4_0,singleton(esk3_0)) != singleton(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])])]) ).
fof(i_0_13,plain,
! [X15,X16] : set_intersection2(X15,X16) = set_intersection2(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_14,plain,
! [X17] : set_intersection2(X17,X17) = X17,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_15,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_9])]) ).
fof(i_0_16,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_17,plain,
( set_intersection2(X2,singleton(X1)) = singleton(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_18,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_19,negated_conjecture,
set_intersection2(esk4_0,singleton(esk3_0)) != singleton(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_20,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_21,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_22,negated_conjecture,
in(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_23,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_24,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_25,axiom,
X1 = X1 ).
cnf(i_0_26,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_27,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_28,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_29,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_30,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_31,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_32,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_33,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_25_001,axiom,
X1 = X1 ).
cnf(i_0_26_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_27_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_28_004,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_29_005,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_30_006,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_31_007,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_32_008,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_33_009,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_34,plain,
$false,
inference(scs_inference,[],[i_0_19,i_0_22,i_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET911+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
% 0.15/0.33 % Computer : n009.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 02:39:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % 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
% 0.25/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------