%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:43:37 PM UTC 2026
% Result : Theorem 33.54s 4.66s
% Output : Proof 33.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 64 unt; 0 def)
% Number of atoms : 81 ( 63 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 7 |; 5 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 114 ( 1 sgn 52 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,conjecture,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th96) ).
fof(f13_neg,negated_conjecture,
~ ! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [B,C] : symmetric_difference(B,C) != difference(union(B,C),intersection(B,C)),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
symmetric_difference(sk2,sk3) != difference(union(sk2,sk3),intersection(sk2,sk3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f13_nnf]) ).
cnf(c28,plain,
symmetric_difference(sk2,sk3) != difference(union(sk2,sk3),intersection(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t152,plain,
eq(symmetric_difference(sk2,sk3),difference(union(sk2,sk3),intersection(sk2,sk3))) = false,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t447,plain,
eq(symmetric_difference(sk2,sk3),difference(union(sk2,sk3),intersection(sk2,sk3))) = false,
inference(orient,[status(thm)],[t152]) ).
cnf(t463,plain,
eq(symmetric_difference(sk2,sk3),difference(union(sk2,sk3),intersection(sk2,sk3))) = false,
inference(rw,[status(thm)],[t447]) ).
fof(f9,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(f9_nnf,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c17,plain,
symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t28,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t477,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(orient,[status(thm)],[t28]) ).
cnf(t880,plain,
eq(symmetric_difference(sk3,sk2),difference(union(sk2,sk3),intersection(sk2,sk3))) = false,
inference(step,[status(thm)],[t463,t477]) ).
fof(f7,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f7_nnf,plain,
! [B,C] : union(B,C) = union(C,B),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] : union(B,C) = union(C,B),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c15,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t29,plain,
union(X1,X2) = union(X2,X1),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t460,plain,
union(X1,X2) = union(X2,X1),
inference(orient,[status(thm)],[t29]) ).
cnf(t881,plain,
eq(symmetric_difference(sk3,sk2),difference(union(sk3,sk2),intersection(sk2,sk3))) = false,
inference(step,[status(thm)],[t880,t460]) ).
fof(f8,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f8_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c16,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t17,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t474,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t17]) ).
cnf(t882,plain,
eq(symmetric_difference(sk3,sk2),difference(union(sk3,sk2),intersection(sk3,sk2))) = false,
inference(step,[status(thm)],[t881,t474]) ).
cnf(t682,plain,
eq(symmetric_difference(sk3,sk2),difference(union(sk3,sk2),intersection(sk3,sk2))) = false,
inference(orient,[status(thm)],[t882]) ).
fof(f2,axiom,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(f2_nnf,plain,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t240,plain,
union(difference(X1,X2),difference(X3,X2)) = difference(union(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t454,plain,
union(difference(X1,X2),difference(X3,X2)) = difference(union(X1,X3),X2),
inference(orient,[status(thm)],[t240]) ).
fof(f1,axiom,
! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_into_intersection) ).
fof(f1_nnf,plain,
! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t39,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t450,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(orient,[status(thm)],[t39]) ).
cnf(t455,plain,
difference(union(X1,X2),intersection(X1,X3)) = union(difference(X1,X3),difference(X2,intersection(X1,X3))),
inference(cp,[status(thm)],[t454,t450]) ).
cnf(t806,plain,
union(difference(X1,X2),difference(X3,intersection(X1,X2))) = difference(union(X1,X3),intersection(X1,X2)),
inference(orient,[status(thm)],[t455]) ).
cnf(t475,plain,
difference(X1,X2) = difference(X1,intersection(X2,X1)),
inference(cp,[status(thm)],[t450,t474]) ).
cnf(t490,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(orient,[status(thm)],[t475]) ).
cnf(t814,plain,
difference(union(X1,X2),intersection(X1,X2)) = union(difference(X1,X2),difference(X2,X1)),
inference(cp,[status(thm)],[t806,t490]) ).
fof(f0,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f0_nnf,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t119,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t466,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(orient,[status(thm)],[t119]) ).
cnf(t887,plain,
difference(union(X1,X2),intersection(X1,X2)) = symmetric_difference(X1,X2),
inference(step,[status(thm)],[t814,t466]) ).
cnf(t831,plain,
difference(union(X1,X2),intersection(X1,X2)) = symmetric_difference(X1,X2),
inference(orient,[status(thm)],[t887]) ).
cnf(t888,plain,
eq(symmetric_difference(sk3,sk2),symmetric_difference(sk3,sk2)) = false,
inference(step,[status(thm)],[t682,t831]) ).
cnf(t2,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t440,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t889,plain,
true = false,
inference(step,[status(thm)],[t888,t440]) ).
cnf(t870,plain,
true = false,
inference(rw,[status(thm)],[t889]) ).
cnf(t871,plain,
false = true,
inference(orient,[status(thm)],[t870]) ).
fof(f5,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f5_nnf,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [D,B,C] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c10,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c28]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t871]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:31:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 33.54/4.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.54/4.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------