%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET977+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 : n004.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 02:44:24 PM UTC 2026
% Result : Theorem 0.13s 6.03s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 97 ( 75 unt; 0 def)
% Number of atoms : 147 ( 99 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 100 ( 50 ~; 28 |; 16 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 138 ( 28 sgn 46 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( B = D
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(f9_nnf,plain,
! [A,B,C,D] :
( ( B != D
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) )
& ( ( B = D
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C,D] :
( ( B != D
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) )
& ( ( B = D
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c14,plain,
( X1 != X3
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t31,plain,
ifeq(in(X1,X2),true,ifeq(X3,X4,in(ordered_pair(X1,X3),cartesian_product2(X2,singleton(X4))),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t44,plain,
ifeq(in(X1,X2),true,ifeq(X3,X4,in(ordered_pair(X1,X3),cartesian_product2(X2,singleton(X4))),true),true) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t17,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t17]) ).
fof(f10,conjecture,
! [A,B] :
( A != empty_set
=> ( cartesian_product2(A,singleton(B)) != empty_set
& cartesian_product2(singleton(B),A) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
fof(f10_neg,negated_conjecture,
~ ! [A,B] :
( A != empty_set
=> ( cartesian_product2(A,singleton(B)) != empty_set
& cartesian_product2(singleton(B),A) != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A,B] :
( ( cartesian_product2(A,singleton(B)) = empty_set
| cartesian_product2(singleton(B),A) = empty_set )
& A != empty_set ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ( cartesian_product2(sk3,singleton(sk4)) = empty_set
| cartesian_product2(singleton(sk4),sk3) = empty_set )
& sk3 != empty_set ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f10_nnf]) ).
cnf(c16,plain,
( cartesian_product2(sk3,singleton(sk4)) = empty_set
| cartesian_product2(singleton(sk4),sk3) = empty_set ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t27,plain,
or(eq(cartesian_product2(singleton(sk4),sk3),empty_set),eq(cartesian_product2(sk3,singleton(sk4)),empty_set)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t59,plain,
or(eq(cartesian_product2(singleton(sk4),sk3),empty_set),eq(cartesian_product2(sk3,singleton(sk4)),empty_set)) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t65,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t16]) ).
fof(f2,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f2_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t21,plain,
or(not(eq(X1,empty_set)),not(in(X2,X1))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t57,plain,
or(not(eq(X1,empty_set)),not(in(X2,X1))) = true,
inference(orient,[status(thm)],[t21]) ).
fof(f8,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f8_nnf,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| A != C
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
& ( ( in(B,D)
& A = C )
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| A != C
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
& ( ( in(B,D)
& A = C )
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c11,plain,
( ~ in(X1,X3)
| X0 != X2
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t30,plain,
ifeq(X1,X2,ifeq(in(X3,X4),true,in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),X4)),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t38,plain,
ifeq(X1,X2,ifeq(in(X3,X4),true,in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),X4)),true),true) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t39,plain,
true = ifeq(in(X1,X2),true,in(ordered_pair(X3,X1),cartesian_product2(singleton(X3),X2)),true),
inference(cp,[status(thm)],[t38,t32]) ).
cnf(t137,plain,
ifeq(in(X1,X2),true,in(ordered_pair(X3,X1),cartesian_product2(singleton(X3),X2)),true) = true,
inference(orient,[status(thm)],[t39]) ).
cnf(c3,plain,
( in(sk0(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t19,plain,
or(eq(X1,empty_set),in(sk0(X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t58,plain,
or(eq(X1,empty_set),in(sk0(X1),X1)) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(c15,plain,
sk3 != empty_set,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t6,plain,
eq(sk3,empty_set) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t68,plain,
eq(sk3,empty_set) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t70,plain,
true = or(false,in(sk0(sk3),sk3)),
inference(cp,[status(thm)],[t58,t68]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t37,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t239,plain,
true = in(sk0(sk3),sk3),
inference(step,[status(thm)],[t70,t37]) ).
cnf(t79,plain,
in(sk0(sk3),sk3) = true,
inference(orient,[status(thm)],[t239]) ).
cnf(t139,plain,
true = ifeq(true,true,in(ordered_pair(X1,sk0(sk3)),cartesian_product2(singleton(X1),sk3)),true),
inference(cp,[status(thm)],[t137,t79]) ).
cnf(t250,plain,
true = in(ordered_pair(X1,sk0(sk3)),cartesian_product2(singleton(X1),sk3)),
inference(step,[status(thm)],[t139,t32]) ).
cnf(t141,plain,
in(ordered_pair(X1,sk0(sk3)),cartesian_product2(singleton(X1),sk3)) = true,
inference(orient,[status(thm)],[t250]) ).
cnf(t143,plain,
true = or(not(eq(cartesian_product2(singleton(X1),sk3),empty_set)),not(true)),
inference(cp,[status(thm)],[t57,t141]) ).
cnf(t4,plain,
not(true) = false,
introduced(definition) ).
cnf(t66,plain,
not(true) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t251,plain,
true = or(not(eq(cartesian_product2(singleton(X1),sk3),empty_set)),false),
inference(step,[status(thm)],[t143,t66]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t36,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t252,plain,
true = not(eq(cartesian_product2(singleton(X1),sk3),empty_set)),
inference(step,[status(thm)],[t251,t36]) ).
cnf(t153,plain,
not(eq(cartesian_product2(singleton(X1),sk3),empty_set)) = true,
inference(orient,[status(thm)],[t252]) ).
cnf(t154,plain,
false = ifeq(true,true,eq(cartesian_product2(singleton(X1),sk3),empty_set),false),
inference(cp,[status(thm)],[t65,t153]) ).
cnf(t253,plain,
false = eq(cartesian_product2(singleton(X1),sk3),empty_set),
inference(step,[status(thm)],[t154,t32]) ).
cnf(t155,plain,
eq(cartesian_product2(singleton(X1),sk3),empty_set) = false,
inference(orient,[status(thm)],[t253]) ).
cnf(t254,plain,
or(false,eq(cartesian_product2(sk3,singleton(sk4)),empty_set)) = true,
inference(step,[status(thm)],[t59,t155]) ).
cnf(t255,plain,
eq(cartesian_product2(sk3,singleton(sk4)),empty_set) = true,
inference(step,[status(thm)],[t254,t37]) ).
cnf(t158,plain,
eq(cartesian_product2(sk3,singleton(sk4)),empty_set) = true,
inference(rw,[status(thm)],[t255]) ).
cnf(t159,plain,
eq(cartesian_product2(sk3,singleton(sk4)),empty_set) = true,
inference(orient,[status(thm)],[t158]) ).
cnf(t160,plain,
empty_set = ifeq(true,true,cartesian_product2(sk3,singleton(sk4)),empty_set),
inference(cp,[status(thm)],[t35,t159]) ).
cnf(t256,plain,
empty_set = cartesian_product2(sk3,singleton(sk4)),
inference(step,[status(thm)],[t160,t32]) ).
cnf(t162,plain,
cartesian_product2(sk3,singleton(sk4)) = empty_set,
inference(orient,[status(thm)],[t256]) ).
cnf(t165,plain,
true = ifeq(in(X1,sk3),true,ifeq(X2,sk4,in(ordered_pair(X1,X2),empty_set),true),true),
inference(cp,[status(thm)],[t44,t162]) ).
cnf(t5,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t61,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t62,plain,
true = or(not(true),not(in(X1,empty_set))),
inference(cp,[status(thm)],[t57,t61]) ).
cnf(t245,plain,
true = or(false,not(in(X1,empty_set))),
inference(step,[status(thm)],[t62,t66]) ).
cnf(t246,plain,
true = not(in(X1,empty_set)),
inference(step,[status(thm)],[t245,t37]) ).
cnf(t109,plain,
not(in(X1,empty_set)) = true,
inference(orient,[status(thm)],[t246]) ).
cnf(t110,plain,
false = ifeq(true,true,in(X1,empty_set),false),
inference(cp,[status(thm)],[t65,t109]) ).
cnf(t247,plain,
false = in(X1,empty_set),
inference(step,[status(thm)],[t110,t32]) ).
cnf(t111,plain,
in(X1,empty_set) = false,
inference(orient,[status(thm)],[t247]) ).
cnf(t266,plain,
true = ifeq(in(X1,sk3),true,ifeq(X2,sk4,false,true),true),
inference(step,[status(thm)],[t165,t111]) ).
cnf(t202,plain,
ifeq(in(X1,sk3),true,ifeq(X2,sk4,false,true),true) = true,
inference(orient,[status(thm)],[t266]) ).
cnf(t203,plain,
true = ifeq(true,true,ifeq(X1,sk4,false,true),true),
inference(cp,[status(thm)],[t202,t79]) ).
cnf(t267,plain,
true = ifeq(X1,sk4,false,true),
inference(step,[status(thm)],[t203,t32]) ).
cnf(t205,plain,
ifeq(X1,sk4,false,true) = true,
inference(orient,[status(thm)],[t267]) ).
cnf(t206,plain,
true = false,
inference(cp,[status(thm)],[t205,t32]) ).
cnf(t208,plain,
false = true,
inference(orient,[status(thm)],[t206]) ).
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(f5,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
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(sk2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f7_nnf]) ).
cnf(c8,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c2,c6,c8,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t208]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n004.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 12:30:14 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/6.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/6.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------