%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:51:04 PM UTC 2026
% Result : Theorem 23.23s 3.81s
% Output : Proof 23.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 33 unt; 0 def)
% Number of atoms : 69 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 17 ~; 13 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 4 sgn 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f54,conjecture,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f54_neg,negated_conjecture,
~ ! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f54_nnf,plain,
? [A,B] :
( ( set_difference(A,B) = A
& ~ disjoint(A,B) )
| ( set_difference(A,B) != A
& disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f54_neg]) ).
fof(f54_sk,plain,
( ( set_difference(sk10,sk11) = sk10
& ~ disjoint(sk10,sk11) )
| ( set_difference(sk10,sk11) != sk10
& disjoint(sk10,sk11) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11])],[f54_nnf]) ).
cnf(c95,plain,
( set_difference(sk10,sk11) = sk10
| disjoint(sk10,sk11) ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f44,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f44_nnf,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c83,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p217,plain,
set_difference(set_union2(X0,X1),X0) = set_difference(X1,X0),
inference(superposition,[status(thm)],[c2,c83]) ).
fof(f46,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f46_nnf,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c85,plain,
set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p396,plain,
set_difference(set_union2(X0,X1),set_difference(X1,X0)) = X0,
inference(superposition,[status(thm)],[p217,c85]) ).
fof(f40,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f40_nnf,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c77,plain,
set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p220,plain,
set_difference(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c77,c83]) ).
cnf(p397,plain,
X0 = set_difference(X0,set_difference(X1,X0)),
inference(demodulation,[status(thm)],[p396,p220]) ).
cnf(p402,plain,
empty_set = set_intersection2(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[p397,c85]) ).
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p408,plain,
set_intersection2(X0,set_difference(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[p402,c3]) ).
fof(f10,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f10_nnf,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c40,plain,
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p148,plain,
( set_intersection2(X1,X0) != empty_set
| disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c3,c40]) ).
cnf(p438,plain,
disjoint(set_difference(X0,X1),X1),
inference(resolution,[status(thm)],[p408,p148]) ).
cnf(p442,plain,
( disjoint(sk10,sk11)
| disjoint(sk10,sk11) ),
inference(superposition,[status(thm)],[c95,p438]) ).
cnf(p449,plain,
disjoint(sk10,sk11),
inference(factoring,[status(thm)],[p442]) ).
cnf(c39,plain,
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p452,plain,
set_intersection2(sk10,sk11) = empty_set,
inference(resolution,[status(thm)],[p449,c39]) ).
cnf(p227,plain,
set_union2(set_intersection2(X0,X1),set_difference(X0,X1)) = X0,
inference(superposition,[status(thm)],[c85,c77]) ).
cnf(p468,plain,
set_difference(sk10,sk11) = sk10,
inference(superposition,[status(thm)],[p452,p227]) ).
cnf(c96,plain,
( ~ disjoint(sk10,sk11)
| set_difference(sk10,sk11) != sk10 ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(p469,plain,
( ~ disjoint(sk10,sk11)
| sk10 != sk10 ),
inference(demodulation,[status(thm)],[p468,c96]) ).
cnf(p475,plain,
~ disjoint(sk10,sk11),
inference(equality_resolution,[status(thm)],[p469]) ).
cnf(p476,plain,
$false,
inference(resolution,[status(thm)],[p475,p449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:57:06 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.23/3.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.23/3.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------