%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:47:45 PM UTC 2026
% Result : Theorem 3.57s 1.74s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f166ERROR: Could not build tree for root c_16558ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> image(X0,domain_of(X0)) = range_of(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> inverse2(X0,range_of(X0)) = domain_of(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
& image4(X0,X1,X2,X0) = range(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f31,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f33,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f35,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p35) ).
fof(f36,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) = domain(X1,X0,X2)
& image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) = range(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_39) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) = domain(X1,X0,X2)
& image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) = range(X1,X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| image(X0,domain_of(X0)) = range_of(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| inverse2(X0,range_of(X0)) = domain_of(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f40,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
& image4(X0,X1,X2,X0) = range(X0,X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f64,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f69,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f71,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f73,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f75,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f77,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,X0))
& ( inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) != domain(X1,X0,X2)
| image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) != range(X1,X0,X2) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f100,plain,
( ilf_type(sK10,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK12,relation_type(sK11,sK10))
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f77]) ).
fof(f101,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| image(X0,domain_of(X0)) = range_of(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f102,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| domain_of(X0) = inverse2(X0,range_of(X0)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X0) = range(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f105,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[],[f41]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f157,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f35]) ).
fof(f160,plain,
ilf_type(sK12,relation_type(sK11,sK10)),
inference(cnf_transformation,[],[f100]) ).
fof(f161,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,[],[f100]) ).
tcf(c_49,plain,
! [X0: $i] :
( ( image(X0,domain_of(X0)) = range_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_50,plain,
! [X0: $i] :
( ( inverse2(X0,range_of(X0)) = domain_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( image4(X1,X2,X0,X1) = range(X1,X2,X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse4(X1,X2,X0,X2) = domain(X1,X2,X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_64,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( image4(X1,X2,X0,X3) = image(X0,X3) )
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse4(X1,X2,X0,X3) = inverse2(X0,X3) )
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_104,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f157]) ).
tcf(c_105,negated_conjecture,
( ( 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,[],[f161]) ).
tcf(c_106,negated_conjecture,
ilf_type(sK12,relation_type(sK11,sK10)),
inference(cnf_transformation,[],[f160]) ).
tcf(c_191,plain,
! [X0: $i] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_104,c_64]) ).
tcf(c_267,plain,
! [X0: $i] :
( ( image(X0,domain_of(X0)) = range_of(X0) )
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_49,c_191]) ).
tcf(c_269,plain,
! [X0: $i] :
( ( inverse2(X0,range_of(X0)) = domain_of(X0) )
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_104,c_64,c_50]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_90,c_104]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_104]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_104]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( image4(X1,X2,X0,X3) = image(X0,X3) )
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_100,c_104]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse4(X1,X2,X0,X3) = inverse2(X0,X3) )
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_104]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_98,c_104]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( image4(X1,X2,X0,X1) = range(X1,X2,X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_104]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse4(X1,X2,X0,X2) = domain(X1,X2,X0) )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_104]) ).
tcf(c_547,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421,c_104]) ).
tcf(c_575,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_422,c_104]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_427,c_104]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_437,c_104]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( image4(X1,X2,X0,X1) = range(X1,X2,X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_438,c_104]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse4(X1,X2,X0,X2) = domain(X1,X2,X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_445,c_104]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( image4(X1,X2,X0,X3) = image(X0,X3) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_432,c_104,c_104]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse4(X1,X2,X0,X3) = inverse2(X0,X3) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_434,c_104,c_104]) ).
tcf(c_1230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( image4(X1,X2,X0,X1) = range(X1,X2,X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_641]) ).
tcf(c_1232,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse4(X1,X2,X0,X2) = domain(X1,X2,X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_652]) ).
tcf(c_1234,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_547,c_575]) ).
tcf(c_1236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = domain_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_619]) ).
tcf(c_1240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = range_of(X0) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_630]) ).
tcf(c_1244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( image4(X1,X2,X0,X3) = image(X0,X3) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_716]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse4(X1,X2,X0,X3) = inverse2(X0,X3) )
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_728]) ).
tcf(c_1256,plain,
! [X0: $i] :
( ( image(X0,domain_of(X0)) = range_of(X0) )
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_267]) ).
tcf(c_1258,plain,
! [X0: $i] :
( ( inverse2(X0,range_of(X0)) = domain_of(X0) )
| ~ relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_269]) ).
tcf(c_2027,definition,
iPr_def_10 = relation_type(sK11,sK10),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2028,definition,
iPr_def_11 = inverse4(sK11,sK10,sK12,sK10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2029,definition,
iPr_def_12 = image4(sK11,sK10,sK12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2030,definition,
iPr_def_13 = range(sK11,sK10,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2031,definition,
iPr_def_14 = image4(sK11,sK10,sK12,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2032,definition,
iPr_def_15 = inverse4(sK11,sK10,sK12,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2033,definition,
iPr_def_16 = domain(sK11,sK10,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2034,negated_conjecture,
ilf_type(sK12,iPr_def_10),
inference(demodulation,[status(thm)],[c_106,c_2027]) ).
tcf(c_2035,negated_conjecture,
( ( iPr_def_15 != iPr_def_16 )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_105,c_2033,c_2031,c_2032,c_2030,c_2028,c_2029]) ).
tcf(c_3103,plain,
! [X0: $i] :
( relation_like(X0)
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2027,c_1234]) ).
tcf(c_3112,plain,
relation_like(sK12),
inference(superposition,[status(thm)],[c_2034,c_3103]) ).
tcf(c_3258,plain,
image(sK12,domain_of(sK12)) = range_of(sK12),
inference(superposition,[status(thm)],[c_3112,c_1256]) ).
tcf(c_3297,plain,
inverse2(sK12,range_of(sK12)) = domain_of(sK12),
inference(superposition,[status(thm)],[c_3112,c_1258]) ).
tcf(c_3389,plain,
! [X0: $i] :
( ( domain(sK11,sK10,X0) = domain_of(X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2027,c_1236]) ).
tcf(c_3417,plain,
! [X0: $i] :
( ( range(sK11,sK10,X0) = range_of(X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2027,c_1240]) ).
tcf(c_3610,plain,
! [X0: $i,X1: $i] :
( ( image4(sK11,sK10,X0,X1) = image(X0,X1) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2027,c_1244]) ).
tcf(c_3642,plain,
! [X0: $i,X1: $i] :
( ( inverse4(sK11,sK10,X0,X1) = inverse2(X0,X1) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2027,c_1248]) ).
tcf(c_3670,plain,
! [X0: $i] :
( ( image4(sK11,sK10,X0,sK11) = range(sK11,sK10,X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2027,c_1230]) ).
tcf(c_3784,plain,
! [X0: $i] :
( ( inverse4(sK11,sK10,X0,sK10) = domain(sK11,sK10,X0) )
| ~ ilf_type(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2027,c_1232]) ).
tcf(c_4132,plain,
domain(sK11,sK10,sK12) = domain_of(sK12),
inference(superposition,[status(thm)],[c_2034,c_3389]) ).
tcf(c_4141,plain,
domain_of(sK12) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_4132,c_2033]) ).
tcf(c_4144,plain,
inverse2(sK12,range_of(sK12)) = iPr_def_16,
inference(demodulation,[status(thm)],[c_3297,c_4141]) ).
tcf(c_4145,plain,
image(sK12,iPr_def_16) = range_of(sK12),
inference(demodulation,[status(thm)],[c_3258,c_4141]) ).
tcf(c_4431,plain,
range(sK11,sK10,sK12) = range_of(sK12),
inference(superposition,[status(thm)],[c_2034,c_3417]) ).
tcf(c_4440,plain,
range_of(sK12) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4431,c_2030]) ).
tcf(c_4443,plain,
image(sK12,iPr_def_16) = iPr_def_13,
inference(demodulation,[status(thm)],[c_4145,c_4440]) ).
tcf(c_4444,plain,
inverse2(sK12,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_4144,c_4440]) ).
tcf(c_6304,plain,
! [X0: $i] : image4(sK11,sK10,sK12,X0) = image(sK12,X0),
inference(superposition,[status(thm)],[c_2034,c_3610]) ).
tcf(c_6315,plain,
image(sK12,sK11) = iPr_def_14,
inference(demodulation,[status(thm)],[c_2031,c_6304]) ).
tcf(c_6316,plain,
image(sK12,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2029,c_6304]) ).
tcf(c_7034,plain,
! [X0: $i] : inverse4(sK11,sK10,sK12,X0) = inverse2(sK12,X0),
inference(superposition,[status(thm)],[c_2034,c_3642]) ).
tcf(c_7045,plain,
inverse2(sK12,sK10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2028,c_7034]) ).
tcf(c_7046,plain,
inverse2(sK12,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_2032,c_7034]) ).
tcf(c_16087,plain,
image4(sK11,sK10,sK12,sK11) = range(sK11,sK10,sK12),
inference(superposition,[status(thm)],[c_2034,c_3670]) ).
tcf(c_16102,plain,
image4(sK11,sK10,sK12,sK11) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_16087,c_2030]) ).
tcf(c_16173,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_16102,c_6304,c_6315]) ).
tcf(c_16200,plain,
inverse2(sK12,iPr_def_13) = iPr_def_15,
inference(demodulation,[status(thm)],[c_7046,c_16173]) ).
tcf(c_16224,plain,
iPr_def_15 = iPr_def_16,
inference(demodulation,[status(thm)],[c_4444,c_16200]) ).
tcf(c_16225,plain,
iPr_def_12 != iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_2035,c_16224]) ).
tcf(c_16267,plain,
image(sK12,iPr_def_15) = iPr_def_13,
inference(demodulation,[status(thm)],[c_4443,c_16224]) ).
tcf(c_16278,plain,
domain(sK11,sK10,sK12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_2033,c_16224]) ).
tcf(c_16474,plain,
inverse4(sK11,sK10,sK12,sK10) = domain(sK11,sK10,sK12),
inference(superposition,[status(thm)],[c_2034,c_3784]) ).
tcf(c_16487,plain,
inverse4(sK11,sK10,sK12,sK10) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_16474,c_16278]) ).
tcf(c_16504,plain,
iPr_def_11 = iPr_def_15,
inference(demodulation,[status(thm)],[c_16487,c_7034,c_7045]) ).
tcf(c_16510,plain,
image(sK12,iPr_def_11) = iPr_def_13,
inference(demodulation,[status(thm)],[c_16267,c_16504]) ).
tcf(c_16557,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_16510,c_6316]) ).
tcf(c_16558,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16557,c_16225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n007.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 11:36:23 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.44
% 0.09/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.44
% 0.09/0.44 % Detected problem language: tptp
% 0.09/0.45 % Proving...
% 3.57/1.74 % SZS status Started for theBenchmark.p
% 3.57/1.74 % SZS status Theorem for theBenchmark.p
% 3.57/1.74
% 3.57/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.57/1.74
% 3.57/1.74 % ------ iProver source info
% 3.57/1.74
% 3.57/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 3.57/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.57/1.74 % git: non_committed_changes: false
% 3.57/1.74
% 3.57/1.74 % ------ Parsing...
% 3.57/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.57/1.74
% 3.57/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.57/1.74
% 3.57/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.57/1.74
% 3.57/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.57/1.74 % ------ Proving...
% 3.57/1.74 % ------ Problem Properties
% 3.57/1.74
% 3.57/1.74 %
% 3.57/1.74 % clauses 50
% 3.57/1.74 % conjectures 2
% 3.57/1.74 % EPR 11
% 3.57/1.74 % Horn 44
% 3.57/1.74 % unary 14
% 3.57/1.74 % binary 31
% 3.57/1.74 % lits 91
% 3.57/1.74 % lits eq 20
% 3.57/1.74 % fd_pure 0
% 3.57/1.74 % fd_pseudo 0
% 3.57/1.74 % fd_cond 0
% 3.57/1.74 % fd_pseudo_cond 1
% 3.57/1.74 % AC symbols 0
% 3.57/1.74
% 3.57/1.74 % ------ Schedule dynamic 5 is on
% 3.57/1.74
% 3.57/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.57/1.74
% 3.57/1.74
% 3.57/1.74 % ------
% 3.57/1.74 % Current options:
% 3.57/1.74 % ------
% 3.57/1.74
% 3.57/1.74
% 3.57/1.74 %
% 3.57/1.74
% 3.57/1.74 % ------ Proving...
% 3.57/1.74 %
% 3.57/1.74
% 3.57/1.74 % SZS status Theorem for theBenchmark.p
% 3.57/1.74
% 3.57/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.57/1.74
% 3.57/1.74
%------------------------------------------------------------------------------