%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Thu Sep 24 02:10:25 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 15 unt; 3 def)
% Number of atoms : 274 ( 69 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 300 ( 124 ~; 122 |; 16 &)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 170 ( 167 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> image(B,domain_of(B)) = range_of(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> inverse2(B,range_of(B)) = domain_of(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,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') ).
fof(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,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/sandbox/benchmark/theBenchmark.p') ).
fof(f27,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/sandbox/benchmark/theBenchmark.p') ).
fof(f29,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/sandbox/benchmark/theBenchmark.p') ).
fof(f31,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/sandbox/benchmark/theBenchmark.p') ).
fof(f33,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/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,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/sandbox/benchmark/theBenchmark.p') ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
! [B] :
( image(B,domain_of(B)) = range_of(B)
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f39,plain,
! [X0] :
( image(X0,domain_of(X0)) = range_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [B] :
( inverse2(B,range_of(B)) = domain_of(B)
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f41,plain,
! [X0] :
( inverse2(X0,range_of(X0)) = domain_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,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(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
! [X0,X1,X2] :
( 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(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( 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(thm)],[f42]) ).
fof(f45,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(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f66,plain,
! [B] :
( ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f67,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)],[f66]) ).
fof(f70,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f115,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(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f116,plain,
! [X0,X1,X2] :
( 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(thm)],[f115]) ).
fof(f127,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(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f128,plain,
! [X0,X1,X2] :
( 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(thm)],[f127]) ).
fof(f131,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(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f132,plain,
! [X0,X1,X2] :
( 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(thm)],[f131]) ).
fof(f135,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(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( 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(thm)],[f135]) ).
fof(f139,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(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( 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(thm)],[f139]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f144,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(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f145,plain,
( ( inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl)) != domain(sK11_skl,sK10_skl,sK12_skl)
| image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl)) != range(sK11_skl,sK10_skl,sK12_skl) )
& ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl))
& ilf_type(sK11_skl,set_type)
& ilf_type(sK10_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(B,sK10_skl),skolemize(C,sK11_skl),skolemize(D,sK12_skl)],[f144]) ).
fof(f148,plain,
ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f149,plain,
( inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl)) != domain(sK11_skl,sK10_skl,sK12_skl)
| image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl)) != range(sK11_skl,sK10_skl,sK12_skl) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f150,definition,
( sQ0_spl
<=> image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl)) = range(sK11_skl,sK10_skl,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ0_spl
| image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl)) != range(sK11_skl,sK10_skl,sK12_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ1_spl
<=> inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl)) = domain(sK11_skl,sK10_skl,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ1_spl
| inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl)) != domain(sK11_skl,sK10_skl,sK12_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f149,f150,f153]) ).
fof(f161,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f70]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f140,f143]) ).
fof(f166,plain,
! [X0,X1,X2,X3] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f136,f143]) ).
fof(f168,plain,
! [X0,X1,X2] :
( range(X0,X2,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f132,f143]) ).
fof(f170,plain,
! [X0,X1,X2] :
( domain(X0,X2,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f128,f143]) ).
fof(f174,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f116,f143]) ).
fof(f190,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f161,f143]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f47,f143]) ).
fof(f197,plain,
! [X0,X1,X2] :
( inverse4(X0,X2,X1,X2) = domain(X0,X2,X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f143]) ).
fof(f198,plain,
! [X0,X1,X2] :
( image4(X0,X2,X1,X0) = range(X0,X2,X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f43,f143]) ).
fof(f201,plain,
! [X0,X1,X2,X3] :
( inverse4(X2,X0,X1,X3) = inverse2(X1,X3)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f143]) ).
fof(f203,plain,
! [X0,X1,X2,X3] :
( image4(X2,X0,X1,X3) = image(X1,X3)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f143]) ).
fof(f205,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f143]) ).
fof(f207,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f143]) ).
fof(f209,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f143]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f143]) ).
fof(f225,plain,
! [X0,X1,X2] :
( inverse4(X1,X2,X0,X2) = domain(X1,X2,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f143]) ).
fof(f226,plain,
! [X0,X1,X2] :
( image4(X1,X2,X0,X1) = range(X1,X2,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f143]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( inverse4(X1,X2,X0,X3) = inverse2(X0,X3)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f201,f143]) ).
fof(f229,plain,
! [X0,X1,X2,X3] :
( image4(X1,X2,X0,X3) = image(X0,X3)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f203,f143]) ).
fof(f230,plain,
range(sK11_skl,sK10_skl,sK12_skl) = range_of(sK12_skl),
inference(resolution,[status(thm)],[f205,f148]) ).
fof(f231,plain,
( sQ0_spl
| image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl)) != range_of(sK12_skl) ),
inference(backward_demodulation,[status(thm)],[f230,f152]) ).
fof(f242,plain,
domain(sK11_skl,sK10_skl,sK12_skl) = domain_of(sK12_skl),
inference(resolution,[status(thm)],[f207,f148]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f209,f190]) ).
fof(f261,plain,
inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl) = domain(sK11_skl,sK10_skl,sK12_skl),
inference(resolution,[status(thm)],[f225,f148]) ).
fof(f264,plain,
( sQ0_spl
| image4(sK11_skl,sK10_skl,sK12_skl,domain_of(sK12_skl)) != range_of(sK12_skl) ),
inference(backward_demodulation,[status(thm)],[f265,f231]) ).
fof(f265,plain,
inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl) = domain_of(sK12_skl),
inference(forward_demodulation,[status(thm)],[f242,f261]) ).
fof(f272,plain,
image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl) = range(sK11_skl,sK10_skl,sK12_skl),
inference(resolution,[status(thm)],[f226,f148]) ).
fof(f275,plain,
image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl) = range_of(sK12_skl),
inference(forward_demodulation,[status(thm)],[f230,f272]) ).
fof(f279,plain,
! [X0] : inverse4(sK11_skl,sK10_skl,sK12_skl,X0) = inverse2(sK12_skl,X0),
inference(resolution,[status(thm)],[f227,f148]) ).
fof(f302,plain,
! [X0] : image4(sK11_skl,sK10_skl,sK12_skl,X0) = image(sK12_skl,X0),
inference(resolution,[status(thm)],[f229,f148]) ).
fof(f305,plain,
image(sK12_skl,sK11_skl) = range_of(sK12_skl),
inference(backward_demodulation,[status(thm)],[f302,f275]) ).
fof(f306,plain,
( sQ0_spl
| image(sK12_skl,domain_of(sK12_skl)) != range_of(sK12_skl) ),
inference(backward_demodulation,[status(thm)],[f302,f264]) ).
fof(f307,plain,
( sQ0_spl
| ~ ilf_type(sK12_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f306,f39]) ).
fof(f308,plain,
! [X0,X1] :
( sQ0_spl
| ~ ilf_type(sK12_skl,subset_type(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f307,f254]) ).
fof(f314,plain,
! [X0,X1] :
( sQ0_spl
| ~ ilf_type(sK12_skl,relation_type(X0,X1)) ),
inference(resolution,[status(thm)],[f308,f223]) ).
fof(f316,plain,
( sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f148,f314]) ).
fof(f317,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f318,plain,
( sQ1_spl
| inverse2(sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl)) != domain(sK11_skl,sK10_skl,sK12_skl) ),
inference(forward_demodulation,[status(thm)],[f279,f155]) ).
fof(f319,plain,
( sQ1_spl
| inverse2(sK12_skl,image(sK12_skl,sK11_skl)) != domain(sK11_skl,sK10_skl,sK12_skl) ),
inference(forward_demodulation,[status(thm)],[f302,f318]) ).
fof(f320,plain,
( sQ1_spl
| inverse2(sK12_skl,range_of(sK12_skl)) != domain(sK11_skl,sK10_skl,sK12_skl) ),
inference(forward_demodulation,[status(thm)],[f305,f319]) ).
fof(f321,plain,
( sQ1_spl
| inverse2(sK12_skl,range_of(sK12_skl)) != domain_of(sK12_skl) ),
inference(forward_demodulation,[status(thm)],[f242,f320]) ).
fof(f337,definition,
( sQ8_spl
<=> ilf_type(sK12_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( ~ sQ8_spl
| ilf_type(sK12_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f339,plain,
( sQ8_spl
| ~ ilf_type(sK12_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f344,plain,
! [X0,X1] :
( sQ8_spl
| ~ ilf_type(sK12_skl,subset_type(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f339,f254]) ).
fof(f345,plain,
! [X0,X1] :
( sQ8_spl
| ~ ilf_type(sK12_skl,relation_type(X0,X1)) ),
inference(resolution,[status(thm)],[f344,f223]) ).
fof(f347,plain,
( sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f148,f345]) ).
fof(f348,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f359,plain,
( ~ sQ8_spl
| inverse2(sK12_skl,range_of(sK12_skl)) = domain_of(sK12_skl) ),
inference(resolution,[status(thm)],[f338,f41]) ).
fof(f360,plain,
( ~ sQ8_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f321]) ).
fof(f361,plain,
( ~ sQ8_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f362,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f317,f348,f361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:36:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.059215 seconds
% 0.14/0.43 % CPU time: 0.205568 seconds
% 0.14/0.43 % Total memory used: 82.032 MB
% 0.14/0.43 % Net memory used: 81.868 MB
%------------------------------------------------------------------------------