%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET638+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n001.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 05:08:12 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 25 unt; 0 def)
% Number of atoms : 40 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 5 ~; 2 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th120,conjecture,
! [X1,X2,X3] :
( ( subset(X1,union(X2,X3))
& intersection(X1,X3) = empty_set )
=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th120) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(intersection_distributes_over_union,axiom,
! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_distributes_over_union) ).
fof(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
fof(subset_intersection,axiom,
! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,union(X2,X3))
& intersection(X1,X3) = empty_set )
=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[prove_th120]) ).
fof(c_0_8,negated_conjecture,
( subset(esk4_0,union(esk5_0,esk6_0))
& intersection(esk4_0,esk6_0) = empty_set
& ~ subset(esk4_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_9,plain,
! [X60,X61] : union(X60,X61) = union(X61,X60),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_10,plain,
! [X42,X43,X44] : intersection(X42,union(X43,X44)) = union(intersection(X42,X43),intersection(X42,X44)),
inference(variable_rename,[status(thm)],[intersection_distributes_over_union]) ).
fof(c_0_11,plain,
! [X41] : union(X41,empty_set) = X41,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_12,plain,
! [X39,X40] :
( ~ subset(X39,X40)
| intersection(X39,X40) = X39 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_intersection])]) ).
cnf(c_0_13,negated_conjecture,
subset(esk4_0,union(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
intersection(esk4_0,esk6_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X37,X38] : subset(intersection(X37,X38),X37),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
fof(c_0_19,plain,
! [X62,X63] : intersection(X62,X63) = intersection(X63,X62),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_20,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
subset(esk4_0,union(esk6_0,esk5_0)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
intersection(esk4_0,union(X1,esk6_0)) = intersection(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
intersection(esk4_0,union(esk6_0,esk5_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
intersection(esk4_0,union(esk6_0,X1)) = intersection(esk4_0,X1),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_27,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
intersection(esk4_0,esk5_0) = esk4_0,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
~ subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET638+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n001.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 02:31:18 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------