%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET617+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 : 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 8.57s 1.72s
% Output : Proof 8.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 22 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 1 sgn 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6_nnf,plain,
! [B,C] : union(B,C) = union(C,B),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,C] : union(B,C) = union(C,B),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c8,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f1,axiom,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
fof(f1_nnf,plain,
! [B] : union(B,empty_set) = B,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] : union(B,empty_set) = B,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
union(X0,empty_set) = X0,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p32,plain,
union(empty_set,X0) = X0,
inference(superposition,[status(thm)],[c8,c1]) ).
fof(f3,axiom,
! [B] : difference(empty_set,B) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
fof(f3_nnf,plain,
! [B] : difference(empty_set,B) = empty_set,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B] : difference(empty_set,B) = empty_set,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f0,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/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(p25,plain,
symmetric_difference(empty_set,X0) = union(empty_set,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(p33,plain,
symmetric_difference(empty_set,X0) = X0,
inference(demodulation,[status(thm)],[p32,p25]) ).
cnf(p26,plain,
symmetric_difference(X0,empty_set) = X0,
inference(superposition,[status(thm)],[c3,c0]) ).
fof(f12,conjecture,
! [B] :
( symmetric_difference(empty_set,B) = B
& symmetric_difference(B,empty_set) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th92) ).
fof(f12_neg,negated_conjecture,
~ ! [B] :
( symmetric_difference(empty_set,B) = B
& symmetric_difference(B,empty_set) = B ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [B] :
( symmetric_difference(empty_set,B) != B
| symmetric_difference(B,empty_set) != B ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( symmetric_difference(empty_set,sk3) != sk3
| symmetric_difference(sk3,empty_set) != sk3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f12_nnf]) ).
cnf(c22,plain,
( symmetric_difference(empty_set,sk3) != sk3
| symmetric_difference(sk3,empty_set) != sk3 ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p27,plain,
( symmetric_difference(empty_set,sk3) != sk3
| sk3 != sk3 ),
inference(demodulation,[status(thm)],[p26,c22]) ).
cnf(p29,plain,
symmetric_difference(empty_set,sk3) != sk3,
inference(equality_resolution,[status(thm)],[p27]) ).
cnf(p39,plain,
$false,
inference(resolution,[status(thm)],[p33,p29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 11:31:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.57/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.57/1.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------