%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET917+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 : 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 02:44:17 PM UTC 2026
% Result : Theorem 4.07s 0.98s
% Output : Proof 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 36 unt; 0 def)
% Number of atoms : 68 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 29 ~; 11 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 60 ( 2 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B] :
( set_intersection2(singleton(A),B) != singleton(A)
& ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( set_intersection2(singleton(sk2),sk3) != singleton(sk2)
& ~ disjoint(singleton(sk2),sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f8_nnf]) ).
cnf(c8,plain,
~ disjoint(singleton(sk2),sk3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t10,plain,
disjoint(singleton(sk2),sk3) = false,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t44,plain,
disjoint(singleton(sk2),sk3) = false,
inference(orient,[status(thm)],[t10]) ).
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t12,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t55,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(orient,[status(thm)],[t12]) ).
fof(f4,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( set_intersection2(X1,singleton(X0)) = singleton(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t22,plain,
ifeq(in(X1,X2),true,set_intersection2(X2,singleton(X1)),singleton(X1)) = singleton(X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t53,plain,
ifeq(in(X1,X2),true,set_intersection2(X2,singleton(X1)),singleton(X1)) = singleton(X1),
inference(orient,[status(thm)],[t22]) ).
fof(f3,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t18,plain,
or(in(X1,X2),disjoint(singleton(X1),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t36,plain,
or(in(X1,X2),disjoint(singleton(X1),X2)) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t47,plain,
true = or(in(sk2,sk3),false),
inference(cp,[status(thm)],[t36,t44]) ).
cnf(t5,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t26,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t79,plain,
true = in(sk2,sk3),
inference(step,[status(thm)],[t47,t26]) ).
cnf(t59,plain,
in(sk2,sk3) = true,
inference(orient,[status(thm)],[t79]) ).
cnf(t60,plain,
singleton(sk2) = ifeq(true,true,set_intersection2(sk3,singleton(sk2)),singleton(sk2)),
inference(cp,[status(thm)],[t53,t59]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t85,plain,
singleton(sk2) = set_intersection2(sk3,singleton(sk2)),
inference(step,[status(thm)],[t60,t24]) ).
cnf(t76,plain,
set_intersection2(sk3,singleton(sk2)) = singleton(sk2),
inference(orient,[status(thm)],[t85]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f6,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f6_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f6_nnf]) ).
cnf(c6,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c9,plain,
set_intersection2(singleton(sk2),sk3) != singleton(sk2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c6,c8,c9]) ).
cnf(g0_0,plain,
true != ifeq(set_intersection2(singleton(sk2),sk3),singleton(sk2),false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(set_intersection2(singleton(sk2),sk3),singleton(sk2),false,ifeq(disjoint(singleton(sk2),sk3),true,false,true)),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
true != ifeq(set_intersection2(singleton(sk2),sk3),singleton(sk2),false,ifeq(false,true,false,true)),
inference(rw,[status(thm)],[g0_1,t44]) ).
cnf(g0_3,plain,
true != ifeq(set_intersection2(sk3,singleton(sk2)),singleton(sk2),false,ifeq(false,true,false,true)),
inference(rw,[status(thm)],[g0_2,t55]) ).
cnf(g0_4,plain,
true != ifeq(set_intersection2(sk3,singleton(sk2)),set_intersection2(sk3,singleton(sk2)),false,ifeq(false,true,false,true)),
inference(rw,[status(thm)],[g0_3,t76]) ).
cnf(g0_5,plain,
true != false,
inference(rw,[status(thm)],[g0_4,t24]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET917+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:22:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.07/0.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.07/0.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------