%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET675+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 : n005.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 02:43:47 PM UTC 2026
% Result : Theorem 40.80s 6.62s
% Output : Proof 40.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 19 unt; 0 def)
% Number of atoms : 275 ( 76 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 328 ( 143 ~; 132 |; 19 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 181 ( 4 sgn 90 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f32_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( inverse4(B,C,D,E) = inverse2(D,E)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [B,C,D,E] :
( inverse4(B,C,D,E) = inverse2(D,E)
| ~ ilf_type(E,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c54,plain,
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f34,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p35) ).
fof(f34_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c56,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p228,plain,
( inverse4(X2,X0,X1,X3) = inverse2(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c54,c56]) ).
cnf(p497,plain,
( inverse4(X1,X2,X0,X3) = inverse2(X0,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p228,c56]) ).
fof(f35,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( inverse4(C,B,D,image4(C,B,D,C)) = domain(C,B,D)
& image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_39) ).
fof(f35_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( inverse4(C,B,D,image4(C,B,D,C)) = domain(C,B,D)
& image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( inverse4(C,B,D,image4(C,B,D,C)) != domain(C,B,D)
| image4(C,B,D,inverse4(C,B,D,B)) != range(C,B,D) )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( inverse4(sk11,sk10,sk12,image4(sk11,sk10,sk12,sk11)) != domain(sk11,sk10,sk12)
| image4(sk11,sk10,sk12,inverse4(sk11,sk10,sk12,sk10)) != range(sk11,sk10,sk12) )
& ilf_type(sk12,relation_type(sk11,sk10))
& ilf_type(sk11,set_type)
& ilf_type(sk10,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12])],[f35_nnf]) ).
cnf(c59,plain,
ilf_type(sk12,relation_type(sk11,sk10)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p1866,plain,
( inverse4(sk11,sk10,sk12,X0) = inverse2(sk12,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p497,c59]) ).
cnf(p1902,plain,
inverse4(sk11,sk10,sk12,X0) = inverse2(sk12,X0),
inference(resolution,[status(thm)],[p1866,c56]) ).
fof(f30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> image4(B,C,D,E) = image(D,E) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f30_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( image4(B,C,D,E) = image(D,E)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [B,C,D,E] :
( image4(B,C,D,E) = image(D,E)
| ~ ilf_type(E,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c52,plain,
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p205,plain,
( image4(X2,X0,X1,X3) = image(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c52,c56]) ).
cnf(p407,plain,
( image4(X1,X2,X0,X3) = image(X0,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p205,c56]) ).
cnf(p1344,plain,
( image4(sk11,sk10,sk12,X0) = image(sk12,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p407,c59]) ).
cnf(p1374,plain,
image4(sk11,sk10,sk12,X0) = image(sk12,X0),
inference(resolution,[status(thm)],[p1344,c56]) ).
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f28_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [B,C,D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c50,plain,
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p192,plain,
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c50,c56]) ).
cnf(p378,plain,
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p192,c56]) ).
cnf(p1187,plain,
range(sk11,sk10,sk12) = range_of(sk12),
inference(resolution,[status(thm)],[p378,c59]) ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( inverse4(B,C,D,C) = domain(B,C,D)
& image4(B,C,D,B) = range(B,C,D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f2_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( inverse4(B,C,D,C) = domain(B,C,D)
& image4(B,C,D,B) = range(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)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( ( inverse4(B,C,D,C) = domain(B,C,D)
& image4(B,C,D,B) = range(B,C,D) )
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p69,plain,
( inverse4(X2,X0,X1,X0) = domain(X2,X0,X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c3,c56]) ).
cnf(p252,plain,
( inverse4(X1,X2,X0,X2) = domain(X1,X2,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p69,c56]) ).
cnf(p283,plain,
inverse4(sk11,sk10,sk12,sk10) = domain_of(sk12),
inference(resolution,[status(thm)],[p252,c59]) ).
cnf(c2,plain,
( image4(X0,X1,X2,X0) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p66,plain,
( image4(X2,X0,X1,X2) = range(X2,X0,X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c2,c56]) ).
cnf(p245,plain,
( image4(X1,X2,X0,X1) = range(X1,X2,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p66,c56]) ).
cnf(p273,plain,
image4(sk11,sk10,sk12,sk11) = range(sk11,sk10,sk12),
inference(resolution,[status(thm)],[p245,c59]) ).
fof(f26,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f26_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [B,C,D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c48,plain,
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p183,plain,
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c48,c56]) ).
cnf(p206,plain,
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p183,c56]) ).
cnf(p207,plain,
domain(sk11,sk10,sk12) = domain_of(sk12),
inference(resolution,[status(thm)],[p206,c59]) ).
cnf(c60,plain,
( inverse4(sk11,sk10,sk12,image4(sk11,sk10,sk12,sk11)) != domain(sk11,sk10,sk12)
| image4(sk11,sk10,sk12,inverse4(sk11,sk10,sk12,sk10)) != range(sk11,sk10,sk12) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p208,plain,
( inverse4(sk11,sk10,sk12,image4(sk11,sk10,sk12,sk11)) != domain_of(sk12)
| image4(sk11,sk10,sk12,inverse4(sk11,sk10,sk12,sk10)) != range(sk11,sk10,sk12) ),
inference(demodulation,[status(thm)],[p207,c60]) ).
cnf(p274,plain,
( inverse4(sk11,sk10,sk12,range(sk11,sk10,sk12)) != domain_of(sk12)
| image4(sk11,sk10,sk12,inverse4(sk11,sk10,sk12,sk10)) != range(sk11,sk10,sk12) ),
inference(demodulation,[status(thm)],[p273,p208]) ).
cnf(p284,plain,
( inverse4(sk11,sk10,sk12,range(sk11,sk10,sk12)) != domain_of(sk12)
| image4(sk11,sk10,sk12,domain_of(sk12)) != range(sk11,sk10,sk12) ),
inference(demodulation,[status(thm)],[p283,p274]) ).
cnf(p1189,plain,
( inverse4(sk11,sk10,sk12,range_of(sk12)) != domain_of(sk12)
| image4(sk11,sk10,sk12,domain_of(sk12)) != range_of(sk12) ),
inference(demodulation,[status(thm)],[p1187,p284]) ).
cnf(p1376,plain,
( inverse4(sk11,sk10,sk12,range_of(sk12)) != domain_of(sk12)
| image(sk12,domain_of(sk12)) != range_of(sk12) ),
inference(demodulation,[status(thm)],[p1374,p1189]) ).
fof(f22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f22_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [B,C,D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c42,plain,
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p116,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c42,c56]) ).
cnf(p121,plain,
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p116,c56]) ).
fof(f3,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/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c5,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)],[f3_sk]) ).
cnf(p76,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)],[c5,c56]) ).
cnf(p106,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p76,c56]) ).
cnf(p107,plain,
ilf_type(sk12,subset_type(cross_product(sk11,sk10))),
inference(resolution,[status(thm)],[p106,c59]) ).
cnf(p124,plain,
relation_like(sk12),
inference(resolution,[status(thm)],[p121,p107]) ).
fof(f11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f11_nnf,plain,
! [B] :
( ( ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [B] :
( ( ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c17,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p87,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(factoring,[status(thm)],[c17]) ).
cnf(p88,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p87,c56]) ).
cnf(p126,plain,
ilf_type(sk12,binary_relation_type),
inference(resolution,[status(thm)],[p124,p88]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> image(B,domain_of(B)) = range_of(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( image(B,domain_of(B)) = range_of(B)
| ~ ilf_type(B,binary_relation_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B] :
( image(B,domain_of(B)) = range_of(B)
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( image(X0,domain_of(X0)) = range_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p127,plain,
image(sk12,domain_of(sk12)) = range_of(sk12),
inference(resolution,[status(thm)],[p126,c0]) ).
cnf(p1385,plain,
inverse4(sk11,sk10,sk12,range_of(sk12)) != domain_of(sk12),
inference(resolution,[status(thm)],[p1376,p127]) ).
cnf(p1904,plain,
inverse2(sk12,range_of(sk12)) != domain_of(sk12),
inference(demodulation,[status(thm)],[p1902,p1385]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> inverse2(B,range_of(B)) = domain_of(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( inverse2(B,range_of(B)) = domain_of(B)
| ~ ilf_type(B,binary_relation_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] :
( inverse2(B,range_of(B)) = domain_of(B)
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( inverse2(X0,range_of(X0)) = domain_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p128,plain,
inverse2(sk12,range_of(sk12)) = domain_of(sk12),
inference(resolution,[status(thm)],[p126,c1]) ).
cnf(p1905,plain,
$false,
inference(resolution,[status(thm)],[p1904,p128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 11:38:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 40.80/6.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.80/6.62 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------