%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:43:40 PM UTC 2026
% Result : Theorem 29.12s 19.12s
% Output : Proof 29.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 29 unt; 0 def)
% Number of atoms : 41 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 5 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_and_intersection) ).
fof(f4_nnf,plain,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f1,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f12,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f12_nnf,plain,
! [B] : subset(B,B),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [B] : subset(B,B),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c21,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p31,plain,
difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[c2,c21]) ).
fof(f3,axiom,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
fof(f3_nnf,plain,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p39,plain,
difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(superposition,[status(thm)],[p31,c4]) ).
cnf(p93,plain,
difference(intersection(X0,X1),X2) = intersection(X0,difference(X1,X2)),
inference(superposition,[status(thm)],[c5,p39]) ).
fof(f10,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f10_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c17,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p57,plain,
intersection(X0,difference(X1,X2)) = difference(intersection(X1,X0),X2),
inference(superposition,[status(thm)],[c17,c5]) ).
cnf(p95,plain,
intersection(X0,difference(X1,X2)) = intersection(X1,difference(X0,X2)),
inference(demodulation,[status(thm)],[p93,p57]) ).
fof(f15,conjecture,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th117) ).
fof(f15_neg,negated_conjecture,
~ ! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f15_nnf,plain,
? [B,C,D] : intersection(B,difference(C,D)) != difference(intersection(B,C),intersection(B,D)),
inference(nnf_transformation,[status(thm)],[f15_neg]) ).
fof(f15_sk,plain,
intersection(sk3,difference(sk4,sk5)) != difference(intersection(sk3,sk4),intersection(sk3,sk5)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f15_nnf]) ).
cnf(c30,plain,
intersection(sk3,difference(sk4,sk5)) != difference(intersection(sk3,sk4),intersection(sk3,sk5)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p50,plain,
intersection(sk3,difference(sk4,sk5)) != intersection(sk3,difference(sk4,intersection(sk3,sk5))),
inference(superposition,[status(thm)],[c5,c30]) ).
cnf(p729,plain,
intersection(sk3,difference(sk4,sk5)) != intersection(sk3,difference(sk4,sk5)),
inference(superposition,[status(thm)],[p95,p50]) ).
cnf(p804,plain,
$false,
inference(equality_resolution,[status(thm)],[p729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/15.39 % Computer : n014.cluster.edu
% 0.12/15.39 % Model : x86_64 x86_64
% 0.12/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.39 % Memory : 8046.5625MB
% 0.12/15.39 % OS : Linux 6.8.0-71-generic
% 0.12/15.39 % CPULimit : 300
% 0.12/15.39 % WCLimit : 300
% 0.12/15.39 % DateTime : Thu Sep 24 11:31:50 UTC 2026
% 0.12/15.39 % CPUTime :
% 0.12/15.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.12/19.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.12/19.12 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------