%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET891+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:44:14 PM UTC 2026
% Result : Theorem 2.46s 0.79s
% Output : Proof 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 38 ( 2 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l52_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
union(unordered_pair(X0,X1)) = set_union2(X0,X1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
union(unordered_pair(X1,X2)) = set_union2(X1,X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t23,plain,
union(unordered_pair(X1,X2)) = set_union2(X1,X2),
inference(orient,[status(thm)],[t6]) ).
fof(f9,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f9_nnf,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
set_union2(singleton(X1),singleton(X2)) = unordered_pair(X1,X2),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t25,plain,
set_union2(singleton(X1),singleton(X2)) = unordered_pair(X1,X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
fof(f7,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f7_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c7,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f8,conjecture,
! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B] : union(unordered_pair(singleton(A),singleton(B))) != unordered_pair(A,B),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
union(unordered_pair(singleton(sk2),singleton(sk3))) != unordered_pair(sk2,sk3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f8_nnf]) ).
cnf(c8,plain,
union(unordered_pair(singleton(sk2),singleton(sk3))) != unordered_pair(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c7,c8]) ).
cnf(g0_0,plain,
true != ifeq(union(unordered_pair(singleton(sk2),singleton(sk3))),unordered_pair(sk2,sk3),false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(set_union2(singleton(sk2),singleton(sk3)),unordered_pair(sk2,sk3),false,true),
inference(rw,[status(thm)],[g0_0,t23]) ).
cnf(g0_2,plain,
true != ifeq(unordered_pair(sk2,sk3),unordered_pair(sk2,sk3),false,true),
inference(rw,[status(thm)],[g0_1,t25]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t12]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET891+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Thu Sep 24 12:20:22 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.46/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.46/0.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------