%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV404+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 03:17:33 PM UTC 2026
% Result : Theorem 76.53s 11.18s
% Output : CNFRefutation 76.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 104 ( 27 unt; 0 def)
% Number of atoms : 260 ( 111 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 272 ( 116 ~; 123 |; 21 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 238 ( 3 sgn 232 !; 6 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(f12,axiom,
! [X0,X1,X2] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax24) ).
fof(f24,axiom,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax36) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( ( ~ contains_slb(X1,findmin_pqp_res(X0))
& X1 != create_slb )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax47) ).
fof(f36,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
& contains_slb(X1,findmin_pqp_res(X0))
& X1 != create_slb )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax48) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
& contains_slb(X1,findmin_pqp_res(X0))
& X1 != create_slb )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax49) ).
fof(f40,axiom,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax52) ).
fof(f41,axiom,
! [X0] : removemin_cpq_res(X0) = findmin_cpq_res(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax53) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ( ok(remove_cpq(triple(X0,X1,X2),X3))
& check_cpq(remove_cpq(triple(X0,X1,X2),X3)) )
=> check_cpq(triple(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_l27) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
=> ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_l34) ).
fof(f44,conjecture,
! [X0,X1,X2] :
( ( ok(removemin_cpq_eff(triple(X0,X1,X2)))
& check_cpq(removemin_cpq_eff(triple(X0,X1,X2))) )
=> check_cpq(triple(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_co) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ok(removemin_cpq_eff(triple(X0,X1,X2)))
& check_cpq(removemin_cpq_eff(triple(X0,X1,X2))) )
=> check_cpq(triple(X0,X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ~ contains_slb(X1,findmin_pqp_res(X0))
& X1 != create_slb )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(rectify,[],[f35]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
& contains_slb(X1,findmin_pqp_res(X0))
& X1 != create_slb )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(rectify,[],[f36]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
& contains_slb(X1,findmin_pqp_res(X0))
& X1 != create_slb )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
inference(rectify,[],[f37]) ).
fof(f54,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f57,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(flattening,[],[f57]) ).
fof(f77,plain,
! [X0,X1,X2] :
( contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(ennf_transformation,[],[f50]) ).
fof(f78,plain,
! [X0,X1,X2] :
( contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(ennf_transformation,[],[f51]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
inference(ennf_transformation,[],[f52]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
inference(flattening,[],[f81]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ~ ok(remove_cpq(triple(X0,X1,X2),X3))
| ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3))
| check_cpq(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ~ ok(remove_cpq(triple(X0,X1,X2),X3))
| ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3))
| check_cpq(triple(X0,X1,X2)) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f43]) ).
fof(f87,plain,
? [X0,X1,X2] :
( ok(removemin_cpq_eff(triple(X0,X1,X2)))
& check_cpq(removemin_cpq_eff(triple(X0,X1,X2)))
& ~ check_cpq(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f88,plain,
? [X0,X1,X2] :
( ok(removemin_cpq_eff(triple(X0,X1,X2)))
& check_cpq(removemin_cpq_eff(triple(X0,X1,X2)))
& ~ check_cpq(triple(X0,X1,X2)) ),
inference(flattening,[],[f87]) ).
fof(f95,plain,
( ok(removemin_cpq_eff(triple(sK0,sK1,sK2)))
& check_cpq(removemin_cpq_eff(triple(sK0,sK1,sK2)))
& ~ check_cpq(triple(sK0,sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f88]) ).
fof(f97,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f99,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f112,plain,
! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
inference(cnf_transformation,[],[f12]) ).
fof(f124,plain,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f24]) ).
fof(f137,plain,
! [X2,X0,X1] :
( contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(cnf_transformation,[],[f78]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(cnf_transformation,[],[f80]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f142,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
inference(cnf_transformation,[],[f40]) ).
fof(f143,plain,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
inference(cnf_transformation,[],[f41]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( ~ ok(remove_cpq(triple(X0,X1,X2),X3))
| ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f145,plain,
! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[],[f86]) ).
fof(f146,plain,
ok(removemin_cpq_eff(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f95]) ).
fof(f147,plain,
check_cpq(removemin_cpq_eff(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f95]) ).
fof(f148,plain,
~ check_cpq(triple(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f95]) ).
fof(f149,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
inference(definition_unfolding,[],[f142,f143]) ).
fof(f153,plain,
check_cpq(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(definition_unfolding,[],[f147,f149]) ).
fof(f154,plain,
ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(definition_unfolding,[],[f146,f149]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
inference(cnf_transformation,[],[f112]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : check_cpq(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f124]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( contains_slb(X1,findmin_pqp_res(X0))
| ( X1 = create_slb )
| ( triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = create_slb )
| ( triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X2)) )
| ~ contains_slb(X1,findmin_pqp_res(X0))
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = create_slb )
| ( triple(X1,update_slb(X0,findmin_pqp_res(X1)),X2) = findmin_cpq_eff(triple(X1,X0,X2)) )
| ~ contains_slb(X0,findmin_pqp_res(X1))
| ~ less_than(lookup_slb(X0,findmin_pqp_res(X1)),findmin_pqp_res(X1)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( check_cpq(triple(X0,X1,X2))
| ~ ok(remove_cpq(triple(X0,X1,X2),X3))
| ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_97,negated_conjecture,
~ check_cpq(triple(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f148]) ).
tcf(c_98,negated_conjecture,
check_cpq(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(cnf_transformation,[],[f153]) ).
tcf(c_99,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(cnf_transformation,[],[f154]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_133]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = create_slb )
| ( triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X2)) )
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_91,c_90,c_91]) ).
tcf(c_181,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( remove_cpq(X0,X2) = remove_cpq(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( triple(X0,X2,X4) = triple(X1,X3,X5) )
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_199,plain,
! [X0: $i,X1: $i] :
( check_cpq(X0)
| ~ check_cpq(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( ok(X0)
| ~ ok(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( check_cpq(X0)
| ~ check_cpq(triple(X1,X2,X3))
| ( X0 != triple(X1,X2,X3) ) ),
inference(instantiation,[status(thm)],[c_199]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = triple(X0,X1,X2) )
| ( X4 != X3 )
| ( triple(X0,X1,X2) != X3 ) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X3,X4,X5))
| ( triple(X0,X1,X2) != triple(X3,X4,X5) ) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_784,plain,
( check_cpq(triple(sK0,sK1,sK2))
| ~ check_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_981,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(triple(sK0,sK1,sK2))
| ~ check_cpq(triple(X0,X1,X2))
| ( triple(sK0,sK1,sK2) != triple(X0,X1,X2) ) ),
inference(instantiation,[status(thm)],[c_365]) ).
tcf(c_1659,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)))
| ~ check_cpq(triple(X0,X1,X2))
| ( findmin_cpq_eff(triple(sK0,sK1,sK2)) != triple(X0,X1,X2) ) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_1706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( triple(sK0,sK1,sK2) = triple(X0,X1,X2) )
| ( sK2 != X2 )
| ( sK1 != X1 )
| ( sK0 != X0 ) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_1917,plain,
findmin_cpq_eff(triple(sK0,sK1,sK2)) = findmin_cpq_eff(triple(sK0,sK1,sK2)),
inference(instantiation,[status(thm)],[c_181]) ).
tcf(c_3729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( check_cpq(remove_cpq(X0,X2))
| ~ check_cpq(remove_cpq(X1,X3))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_195,c_199]) ).
tcf(c_3730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ok(remove_cpq(X0,X2))
| ~ ok(remove_cpq(X1,X3))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_195,c_201]) ).
tcf(c_6881,plain,
sK2 = sK2,
inference(instantiation,[status(thm)],[c_181]) ).
tcf(c_7914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( findmin_cpq_eff(triple(sK0,sK1,sK2)) = triple(X1,X2,X3) )
| ( triple(X1,X2,X3) != X0 )
| ( findmin_cpq_eff(triple(sK0,sK1,sK2)) != X0 ) ),
inference(instantiation,[status(thm)],[c_364]) ).
tcf(c_17970,plain,
! [X0: $i,X1: $i] :
( ( triple(sK0,sK1,sK2) = triple(sK0,X0,X1) )
| ( sK2 != X1 )
| ( sK1 != X0 )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_1706]) ).
tcf(c_17971,plain,
sK0 = sK0,
inference(instantiation,[status(thm)],[c_181]) ).
tcf(c_19463,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( findmin_cpq_eff(triple(sK0,sK1,sK2)) = triple(X0,X1,X2) )
| ( triple(X0,X1,X2) != findmin_cpq_eff(triple(sK0,sK1,sK2)) )
| ( findmin_cpq_eff(triple(sK0,sK1,sK2)) != findmin_cpq_eff(triple(sK0,sK1,sK2)) ) ),
inference(instantiation,[status(thm)],[c_7914]) ).
tcf(c_27017,plain,
! [X0: $i] :
( ( triple(sK0,sK1,sK2) = triple(sK0,X0,sK2) )
| ( sK2 != sK2 )
| ( sK1 != X0 )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_17970]) ).
tcf(c_27018,plain,
( ( triple(sK0,sK1,sK2) = triple(sK0,create_slb,sK2) )
| ( sK2 != sK2 )
| ( sK1 != create_slb )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_27017]) ).
tcf(c_27687,plain,
! [X0: $i,X1: $i] :
( check_cpq(triple(sK0,sK1,sK2))
| ~ check_cpq(triple(X0,X1,sK2))
| ( triple(sK0,sK1,sK2) != triple(X0,X1,sK2) ) ),
inference(instantiation,[status(thm)],[c_981]) ).
tcf(c_30770,plain,
! [X0: $i,X1: $i] :
( check_cpq(remove_cpq(X0,X1))
| ( X1 != removemin_cpq_res(triple(sK0,sK1,sK2)) )
| ( X0 != findmin_cpq_eff(triple(sK0,sK1,sK2)) ) ),
inference(resolution,[status(thm)],[c_3729,c_98]) ).
tcf(c_30838,plain,
! [X0: $i,X1: $i] :
( ok(remove_cpq(X0,X1))
| ( X1 != removemin_cpq_res(triple(sK0,sK1,sK2)) )
| ( X0 != findmin_cpq_eff(triple(sK0,sK1,sK2)) ) ),
inference(resolution,[status(thm)],[c_3730,c_99]) ).
tcf(c_30924,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(remove_cpq(X0,remove_slb(insert_slb(removemin_cpq_res(triple(sK0,sK1,sK2)),pair(X1,X2)),X1)))
| ( X0 != findmin_cpq_eff(triple(sK0,sK1,sK2)) ) ),
inference(resolution,[status(thm)],[c_30770,c_65]) ).
tcf(c_31223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ok(remove_cpq(X0,remove_slb(insert_slb(removemin_cpq_res(triple(sK0,sK1,sK2)),pair(X1,X2)),X1)))
| ( X0 != findmin_cpq_eff(triple(sK0,sK1,sK2)) ) ),
inference(resolution,[status(thm)],[c_30838,c_65]) ).
tcf(c_34178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(remove_cpq(triple(X0,X1,X2),remove_slb(insert_slb(removemin_cpq_res(triple(sK0,sK1,sK2)),pair(X3,X4)),X3)))
| ( triple(X0,X1,X2) != findmin_cpq_eff(triple(sK0,sK1,sK2)) ) ),
inference(resolution,[status(thm)],[c_95,c_31223]) ).
tcf(c_38367,plain,
! [X0: $i] : check_cpq(triple(X0,create_slb,sK2)),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_42988,plain,
! [X0: $i] :
( check_cpq(triple(sK0,sK1,sK2))
| ~ check_cpq(triple(sK0,X0,sK2))
| ( triple(sK0,sK1,sK2) != triple(sK0,X0,sK2) ) ),
inference(instantiation,[status(thm)],[c_27687]) ).
tcf(c_42991,plain,
( check_cpq(triple(sK0,sK1,sK2))
| ~ check_cpq(triple(sK0,create_slb,sK2))
| ( triple(sK0,sK1,sK2) != triple(sK0,create_slb,sK2) ) ),
inference(instantiation,[status(thm)],[c_42988]) ).
tcf(c_45395,plain,
( strictly_less_than(findmin_pqp_res(sK0),lookup_slb(sK1,findmin_pqp_res(sK0)))
| less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0)) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_50564,plain,
check_cpq(triple(sK0,create_slb,sK2)),
inference(instantiation,[status(thm)],[c_38367]) ).
tcf(c_85287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( triple(X0,X1,X2) != findmin_cpq_eff(triple(sK0,sK1,sK2)) )
| ~ check_cpq(remove_cpq(triple(X0,X1,X2),remove_slb(insert_slb(removemin_cpq_res(triple(sK0,sK1,sK2)),pair(X3,X4)),X3))) ),
inference(global_subsumption_just,[status(thm)],[c_34178,c_97,c_784,c_1659,c_1917,c_19463,c_34178]) ).
tcf(c_85288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ check_cpq(remove_cpq(triple(X0,X1,X2),remove_slb(insert_slb(removemin_cpq_res(triple(sK0,sK1,sK2)),pair(X3,X4)),X3)))
| ( triple(X0,X1,X2) != findmin_cpq_eff(triple(sK0,sK1,sK2)) ) ),
inference(renaming,[status(thm)],[c_85287]) ).
tcf(c_85292,plain,
! [X0: $i,X1: $i,X2: $i] : triple(X0,X1,X2) != findmin_cpq_eff(triple(sK0,sK1,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_85288,c_30924]) ).
tcf(c_85538,plain,
( contains_slb(sK1,findmin_pqp_res(sK0))
| ( sK1 = create_slb ) ),
inference(resolution,[status(thm)],[c_85292,c_90]) ).
tcf(c_85539,plain,
( ( sK1 = create_slb )
| ~ strictly_less_than(findmin_pqp_res(sK0),lookup_slb(sK1,findmin_pqp_res(sK0))) ),
inference(resolution,[status(thm)],[c_85292,c_135]) ).
tcf(c_85540,plain,
( ( sK1 = create_slb )
| ~ contains_slb(sK1,findmin_pqp_res(sK0))
| ~ less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0)) ),
inference(resolution,[status(thm)],[c_85292,c_92]) ).
tcf(c_85541,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_85540,c_85538,c_85539,c_50564,c_45395,c_42991,c_27018,c_17971,c_6881,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV404+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 19:29:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.33
% 0.06/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.06/0.33
% 0.06/0.33 % Detected problem language: tptp
% 0.06/0.34 % Proving...
% 76.53/11.18 % SZS status Started for theBenchmark.p
% 76.53/11.18 % SZS status Theorem for theBenchmark.p
% 76.53/11.18
% 76.53/11.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 76.53/11.18
% 76.53/11.18 % ------ iProver source info
% 76.53/11.18
% 76.53/11.18 % git: date: 2026-07-19 20:42:38 +0200
% 76.53/11.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 76.53/11.18 % git: non_committed_changes: false
% 76.53/11.18
% 76.53/11.18 % ------ Parsing...
% 76.53/11.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 76.53/11.18
% 76.53/11.18 % ------ Preprocessing... sf_s rm: 7 0s sf_e sf_s rm: 2 0s sf_e %
% 76.53/11.18
% 76.53/11.18 % ------ Preprocessing...%
% 76.53/11.18
% 76.53/11.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 76.53/11.18 % ------ Proving...
% 76.53/11.18 % ------ Problem Properties
% 76.53/11.18
% 76.53/11.18 %
% 76.53/11.18 % clauses 46
% 76.53/11.18 % conjectures 3
% 76.53/11.18 % EPR 8
% 76.53/11.18 % Horn 33
% 76.53/11.18 % unary 19
% 76.53/11.18 % binary 13
% 76.53/11.18 % lits 88
% 76.53/11.18 % lits eq 27
% 76.53/11.18 % fd_pure 0
% 76.53/11.18 % fd_pseudo 0
% 76.53/11.18 % fd_cond 5
% 76.53/11.18 % fd_pseudo_cond 5
% 76.53/11.18 % AC symbols 0
% 76.53/11.18
% 76.53/11.18 % ------ Input Options Time Limit: Unbounded
% 76.53/11.18
% 76.53/11.18
% 76.53/11.18 % ------
% 76.53/11.18 % Current options:
% 76.53/11.18 % ------
% 76.53/11.18
% 76.53/11.18
% 76.53/11.18 %
% 76.53/11.18
% 76.53/11.18 % ------ Proving...
% 76.53/11.18 %
% 76.53/11.18
% 76.53/11.18 % SZS status Theorem for theBenchmark.p
% 76.53/11.18
% 76.53/11.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 76.53/11.18
% 76.53/11.18
%------------------------------------------------------------------------------