%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET656+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 : n018.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 02:43:44 PM UTC 2026
% Result : Theorem 32.53s 4.64s
% Output : Proof 32.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 13 unt; 0 def)
% Number of atoms : 246 ( 13 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 296 ( 116 ~; 121 |; 29 &)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 2 sgn 60 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f18_nnf,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk8(B,C),C)
& member(sk8(B,C),B)
& ilf_type(sk8(B,C),set_type) )
| member(B,power_set(C)) )
& ( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f18_nnf]) ).
cnf(c39,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f29,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
fof(f29_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c68,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p196,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c39,c68]) ).
cnf(p666,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p196,c68]) ).
fof(f20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f20_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [B,C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c45,plain,
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p216,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c45,c68]) ).
cnf(p257,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p216,c68]) ).
fof(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f12_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [B,C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c29,plain,
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p169,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c29,c68]) ).
cnf(p214,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p169,c68]) ).
fof(f5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f5_nnf,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C,D,E] :
( ( ( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c13,plain,
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p135,plain,
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c13,c68]) ).
cnf(p136,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p135,c68]) ).
fof(f30,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> intersection(D,cross_product(B,C)) = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_18) ).
fof(f30_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> intersection(D,cross_product(B,C)) = D ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( intersection(D,cross_product(B,C)) != D
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
( intersection(sk17,cross_product(sk15,sk16)) != sk17
& ilf_type(sk17,relation_type(sk15,sk16))
& ilf_type(sk16,set_type)
& ilf_type(sk15,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15,sk16,sk17])],[f30_nnf]) ).
cnf(c71,plain,
ilf_type(sk17,relation_type(sk15,sk16)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p137,plain,
ilf_type(sk17,subset_type(cross_product(sk15,sk16))),
inference(resolution,[status(thm)],[p136,c71]) ).
cnf(p218,plain,
ilf_type(sk17,member_type(power_set(cross_product(sk15,sk16)))),
inference(resolution,[status(thm)],[p214,p137]) ).
cnf(p259,plain,
( member(sk17,power_set(cross_product(sk15,sk16)))
| empty(power_set(cross_product(sk15,sk16))) ),
inference(resolution,[status(thm)],[p257,p218]) ).
cnf(p2792,plain,
( empty(power_set(cross_product(sk15,sk16)))
| member(X0,cross_product(sk15,sk16))
| ~ member(X0,sk17)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p666,p259]) ).
cnf(p2816,plain,
( empty(power_set(cross_product(sk15,sk16)))
| member(X0,cross_product(sk15,sk16))
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p2792,c68]) ).
fof(f16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(f16_nnf,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk7(B,C),C)
& member(sk7(B,C),B)
& ilf_type(sk7(B,C),set_type) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type)
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f16_nnf]) ).
cnf(c36,plain,
( member(sk7(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p143,plain,
( member(sk7(X1,X0),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c36,c68]) ).
cnf(p144,plain,
( member(sk7(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p143,c68]) ).
cnf(p2818,plain,
( subset(sk17,X0)
| empty(power_set(cross_product(sk15,sk16)))
| member(sk7(sk17,X0),cross_product(sk15,sk16)) ),
inference(resolution,[status(thm)],[p2816,p144]) ).
cnf(c37,plain,
( ~ member(sk7(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p145,plain,
( ~ member(sk7(X1,X0),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c37,c68]) ).
cnf(p146,plain,
( ~ member(sk7(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p145,c68]) ).
cnf(p2869,plain,
( subset(sk17,cross_product(sk15,sk16))
| subset(sk17,cross_product(sk15,sk16))
| empty(power_set(cross_product(sk15,sk16))) ),
inference(resolution,[status(thm)],[p2818,p146]) ).
cnf(p2872,plain,
( subset(sk17,cross_product(sk15,sk16))
| empty(power_set(cross_product(sk15,sk16))) ),
inference(factoring,[status(thm)],[p2869]) ).
fof(f19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f19_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c43,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p76,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c43,c68]) ).
cnf(p2892,plain,
subset(sk17,cross_product(sk15,sk16)),
inference(resolution,[status(thm)],[p2872,p76]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
=> intersection(B,C) = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( intersection(B,C) = B
| ~ subset(B,C)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] :
( intersection(B,C) = B
| ~ subset(B,C)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p74,plain,
( intersection(X1,X0) = X1
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c0,c68]) ).
cnf(p108,plain,
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p74,c68]) ).
cnf(p2893,plain,
intersection(sk17,cross_product(sk15,sk16)) = sk17,
inference(resolution,[status(thm)],[p2892,p108]) ).
cnf(c72,plain,
intersection(sk17,cross_product(sk15,sk16)) != sk17,
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p2894,plain,
sk17 != sk17,
inference(demodulation,[status(thm)],[p2893,c72]) ).
cnf(p2896,plain,
$false,
inference(equality_resolution,[status(thm)],[p2894]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET656+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n018.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 11:36:48 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 32.53/4.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.53/4.64 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------