%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET633+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 : n011.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 6.89s 16.81s
% Output : Proof 6.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 65 ( 20 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 50 ( 21 ~; 13 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 54 ( 3 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [B,C,D] :
( ( subset(difference(C,B),D)
& subset(difference(B,C),D) )
=> subset(symmetric_difference(B,C),D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th115) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(difference(C,B),D)
& subset(difference(B,C),D) )
=> subset(symmetric_difference(B,C),D) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C,D] :
( ~ subset(symmetric_difference(B,C),D)
& subset(difference(C,B),D)
& subset(difference(B,C),D) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ~ subset(symmetric_difference(sk2,sk3),sk4)
& subset(difference(sk3,sk2),sk4)
& subset(difference(sk2,sk3),sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f8_nnf]) ).
cnf(c19,plain,
~ subset(symmetric_difference(sk2,sk3),sk4),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t24,plain,
ifeq(subset(symmetric_difference(sk2,sk3),sk4),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
fof(f1,axiom,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_subset) ).
fof(f1_nnf,plain,
! [B,C,D] :
( subset(union(B,D),C)
| ~ subset(D,C)
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( subset(union(B,D),C)
| ~ subset(D,C)
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi0,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X2,X1),true,subset(union(X0,X2),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c17,plain,
subset(difference(sk2,sk3),sk4),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi14,negated_conjecture,
subset(difference(sk2,sk3),sk4) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(c18,plain,
subset(difference(sk3,sk2),sk4),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi15,negated_conjecture,
subset(difference(sk3,sk2),sk4) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t29,plain,
subset(union(difference(sk2,sk3),difference(sk3,sk2)),sk4) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi14,hi15]) ).
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(t47,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t181,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(orient,[status(thm)],[t47]) ).
cnf(t426,plain,
subset(symmetric_difference(sk2,sk3),sk4) = true,
inference(step,[status(thm)],[t29,t181]) ).
cnf(t236,plain,
subset(symmetric_difference(sk2,sk3),sk4) = true,
inference(orient,[status(thm)],[t426]) ).
cnf(t428,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t24,t236]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t175,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t429,plain,
false = true,
inference(step,[status(thm)],[t428,t175]) ).
cnf(t397,plain,
false = true,
inference(orient,[status(thm)],[t429]) ).
fof(f2,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(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c3,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t397]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET633+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.64 % CPULimit : 300
% 0.09/15.64 % WCLimit : 300
% 0.09/15.64 % DateTime : Thu Sep 24 11:31:46 UTC 2026
% 0.09/15.65 % CPUTime :
% 0.09/15.65 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.89/16.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.89/16.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------