%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV407+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 : 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 03:17:34 PM UTC 2026
% Result : Theorem 127.89s 18.00s
% Output : CNFRefutation 127.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 190 ( 27 unt; 0 def)
% Number of atoms : 532 ( 118 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 561 ( 219 ~; 286 |; 38 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 380 ( 4 sgn 367 !; 13 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X1,X2)
& less_than(X0,X1) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',transitivity) ).
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(f3,axiom,
! [X0] : less_than(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',reflexivity) ).
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(f8,axiom,
! [X0] : ~ contains_slb(create_slb,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax20) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
<=> ( X1 = X2
| contains_slb(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax21) ).
fof(f27,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_slb(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax39) ).
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(f39,axiom,
! [X0,X1,X2,X3] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(f42,axiom,
! [X0,X1,X2] :
( check_cpq(triple(X0,X1,X2))
<=> ! [X3,X4] :
( pair_in_list(X1,X3,X4)
=> less_than(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l43_li4142) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ? [X4] :
( less_than(findmin_pqp_res(X0),X4)
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l43_l44) ).
fof(f44,conjecture,
! [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
=> ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l43_co) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
=> ~ check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f48,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(f49,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(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] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
inference(rectify,[],[f39]) ).
fof(f52,plain,
! [X0,X1,X2] :
( check_cpq(triple(X0,X1,X2))
<=> ! [X3,X4] :
( ~ pair_in_list(X1,X3,X4)
| less_than(X4,X3) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_slb(X1,X3)
| ? [X4] :
( less_than(findmin_pqp_res(X0),X4)
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_slb(X1,X3)
| ? [X4] :
( less_than(findmin_pqp_res(X0),X4)
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
? [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
& check_cpq(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f45]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(flattening,[],[f56]) ).
fof(f60,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,[],[f48]) ).
fof(f61,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,[],[f60]) ).
fof(f63,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,[],[f49]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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(f66,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,[],[f65]) ).
fof(f68,plain,
! [X0,X1,X2] :
( create_slb = X1
| findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( ~ check_cpq(triple(X0,X1,X2))
| ! [X3,X4] :
( ~ pair_in_list(X1,X3,X4)
| less_than(X4,X3) ) )
& ( ? [X3,X4] :
( pair_in_list(X1,X3,X4)
& ~ less_than(X4,X3) )
| check_cpq(triple(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( ~ check_cpq(triple(X0,X1,X2))
| ! [X5,X6] :
( ~ pair_in_list(X1,X5,X6)
| less_than(X6,X5) ) )
& ( ? [X3,X4] :
( pair_in_list(X1,X3,X4)
& ~ less_than(X4,X3) )
| check_cpq(triple(X0,X1,X2)) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( ~ check_cpq(triple(X0,X1,X2))
| ! [X5,X6] :
( ~ pair_in_list(X1,X5,X6)
| less_than(X6,X5) ) )
& ( ( pair_in_list(X1,sK0(X1),sK1(X1))
& ~ less_than(sK1(X1),sK0(X1)) )
| check_cpq(triple(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X1)),skolemize(X4,sK1(X1))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_slb(X1,X3)
| ( less_than(findmin_pqp_res(X0),sK2(X0,X1,X3))
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,sK2(X0,X1,X3)) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X4,sK2(X0,X1,X3))],[f54]) ).
fof(f78,plain,
( strictly_less_than(sK6,findmin_cpq_res(triple(sK3,sK4,sK5)))
& contains_cpq(triple(sK3,sK4,sK5),sK6)
& check_cpq(findmin_cpq_eff(triple(sK3,sK4,sK5))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f55]) ).
fof(f82,plain,
! [X0,X1] :
( ( ~ strictly_less_than(X0,X1)
| ( ~ less_than(X1,X0)
& less_than(X0,X1) ) )
& ( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f83,plain,
! [X0,X1] :
( ( ~ strictly_less_than(X0,X1)
| ( ~ less_than(X1,X0)
& less_than(X0,X1) ) )
& ( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) )
& ( ( X1 != X2
& ~ contains_slb(X0,X2) )
| contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) )
& ( ( X1 != X2
& ~ contains_slb(X0,X2) )
| contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) )
& ( ~ contains_slb(X1,X3)
| contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f87,plain,
! [X2,X0,X1,X6,X5] :
( ~ check_cpq(triple(X0,X1,X2))
| ~ pair_in_list(X1,X5,X6)
| less_than(X6,X5) ),
inference(cnf_transformation,[],[f76]) ).
fof(f88,plain,
! [X2,X0,X1] :
( pair_in_list(X1,sK0(X1),sK1(X1))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ less_than(sK1(X1),sK0(X1))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_slb(X1,X3)
| less_than(findmin_pqp_res(X0),sK2(X0,X1,X3))
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_slb(X1,X3)
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,sK2(X0,X1,X3))
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f92,plain,
strictly_less_than(sK6,findmin_cpq_res(triple(sK3,sK4,sK5))),
inference(cnf_transformation,[],[f78]) ).
fof(f93,plain,
contains_cpq(triple(sK3,sK4,sK5),sK6),
inference(cnf_transformation,[],[f78]) ).
fof(f94,plain,
check_cpq(findmin_cpq_eff(triple(sK3,sK4,sK5))),
inference(cnf_transformation,[],[f78]) ).
fof(f95,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f96,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f107,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,[],[f61]) ).
fof(f109,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ less_than(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f111,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( X1 != X2
| contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f115,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f116,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,[],[f64]) ).
fof(f117,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,[],[f66]) ).
fof(f120,plain,
! [X2,X0,X1] :
( create_slb = X1
| findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f86]) ).
fof(f132,plain,
! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
inference(equality_resolution,[],[f113]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(triple(X1,X0,X2))
| ~ less_than(sK1(X0),sK0(X0)) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(triple(X1,X0,X2))
| pair_in_list(X0,sK0(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_than(X4,X3)
| ~ pair_in_list(X1,X3,X4)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X0,findmin_pqp_res(X1))
| pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X0,sK2(X1,X2,X0))
| ~ contains_slb(X2,X0)
| ~ strictly_less_than(X0,findmin_cpq_res(triple(X1,X2,X3))) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(findmin_pqp_res(X1),sK2(X1,X2,X0))
| pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X0,findmin_pqp_res(X1))
| ~ contains_slb(X2,X0)
| ~ strictly_less_than(X0,findmin_cpq_res(triple(X1,X2,X3))) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_54,negated_conjecture,
check_cpq(findmin_cpq_eff(triple(sK3,sK4,sK5))),
inference(cnf_transformation,[],[f94]) ).
tcf(c_55,negated_conjecture,
contains_cpq(triple(sK3,sK4,sK5),sK6),
inference(cnf_transformation,[],[f93]) ).
tcf(c_56,negated_conjecture,
strictly_less_than(sK6,findmin_cpq_res(triple(sK3,sK4,sK5))),
inference(cnf_transformation,[],[f92]) ).
tcf(c_57,plain,
! [X0: $i] : less_than(X0,X0),
inference(cnf_transformation,[],[f95]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_69,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,[],[f107]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ~ strictly_less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : contains_slb(insert_slb(X0,pair(X1,X2)),X1),
inference(cnf_transformation,[],[f132]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( contains_slb(X0,X3)
| ( X1 = X3 )
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_77,plain,
! [X0: $i] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f115]) ).
tcf(c_78,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,[],[f116]) ).
tcf(c_79,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,[],[f117]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = create_slb )
| ( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_94,plain,
~ contains_slb(create_slb,create_slb),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_98,plain,
contains_slb(insert_slb(create_slb,pair(create_slb,create_slb)),create_slb),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_109,plain,
( contains_slb(create_slb,create_slb)
| ( create_slb = create_slb )
| ~ contains_slb(insert_slb(create_slb,pair(create_slb,create_slb)),create_slb) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_58,c_71]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_117]) ).
tcf(c_119,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_69,c_79,c_69]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_118]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_124]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i,X2: $i] :
( strictly_less_than(X0,X2)
| less_than(X2,X1)
| ~ less_than(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_59,c_125]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_118]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_624]) ).
tcf(c_740,plain,
! [X0: $i,X1: $i,X2: $i] :
( strictly_less_than(X2,X0)
| strictly_less_than(X1,X2)
| less_than(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_257,c_625]) ).
tcf(c_1798,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1800,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1802,plain,
! [X0: $i,X1: $i] :
( check_cpq(X0)
| ~ check_cpq(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(X0,X2)
| ~ less_than(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( contains_slb(X0,X2)
| ~ contains_slb(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1823,plain,
! [X0: $i,X1: $i] :
( ~ less_than(X0,X1)
| ~ strictly_less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
tcf(c_1824,plain,
! [X0: $i,X1: $i] :
( ~ strictly_less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_1823]) ).
tcf(c_1982,plain,
! [X0: $i,X1: $i,X2: $i] :
( strictly_less_than(X2,X1)
| strictly_less_than(X0,X2)
| ~ strictly_less_than(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_740,c_1824]) ).
tcf(c_2660,plain,
! [X0: $i] : ~ strictly_less_than(X0,X0),
inference(superposition,[status(thm)],[c_57,c_73]) ).
tcf(c_2813,plain,
contains_slb(sK4,sK6),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_2819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( strictly_less_than(X3,sK1(X1))
| strictly_less_than(sK0(X1),X3)
| check_cpq(triple(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_740,c_49]) ).
tcf(c_3171,plain,
( ~ strictly_less_than(sK6,findmin_cpq_res(triple(sK3,sK4,sK5)))
| ~ less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),sK6) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_3173,plain,
! [X0: $i] :
( check_cpq(X0)
| ~ check_cpq(findmin_cpq_eff(triple(sK3,sK4,sK5)))
| ( X0 != findmin_cpq_eff(triple(sK3,sK4,sK5)) ) ),
inference(instantiation,[status(thm)],[c_1802]) ).
tcf(c_3180,plain,
! [X0: $i] :
( strictly_less_than(sK6,X0)
| strictly_less_than(X0,findmin_cpq_res(triple(sK3,sK4,sK5)))
| ~ strictly_less_than(sK6,findmin_cpq_res(triple(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_1982]) ).
tcf(c_3199,plain,
! [X0: $i,X1: $i,X2: $i] :
( strictly_less_than(sK0(X1),sK1(X1))
| check_cpq(triple(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2819,c_2660]) ).
tcf(c_3341,plain,
! [X0: $i,X1: $i] :
( less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),sK6)
| ~ less_than(X0,X1)
| ( sK6 != X1 )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1803]) ).
tcf(c_3399,plain,
! [X0: $i,X1: $i] :
( contains_slb(X0,X1)
| ~ contains_slb(sK4,sK6)
| ( X1 != sK6 )
| ( X0 != sK4 ) ),
inference(instantiation,[status(thm)],[c_1806]) ).
tcf(c_3672,plain,
sK6 = sK6,
inference(instantiation,[status(thm)],[c_1798]) ).
tcf(c_4264,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X2,X1)
| pair_in_list(X0,sK0(X0),sK1(X0))
| ~ pair_in_list(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_4398,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X2,X1)
| strictly_less_than(sK0(X0),sK1(X0))
| ~ pair_in_list(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_3199,c_51]) ).
tcf(c_5050,plain,
! [X0: $i] :
( less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),sK6)
| ~ less_than(X0,sK6)
| ( sK6 != sK6 )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) != X0 ) ),
inference(instantiation,[status(thm)],[c_3341]) ).
tcf(c_5298,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK4 )
| ( sK4 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1800]) ).
tcf(c_5299,plain,
( ( create_slb = sK4 )
| ( create_slb != create_slb )
| ( sK4 != create_slb ) ),
inference(instantiation,[status(thm)],[c_5298]) ).
tcf(c_7421,plain,
( less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ contains_slb(sK4,sK6) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
tcf(c_7467,plain,
( less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7421,c_2813]) ).
tcf(c_7877,plain,
( pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,sK2(sK3,sK4,sK6))
| ~ contains_slb(sK4,sK6) ),
inference(superposition,[status(thm)],[c_56,c_52]) ).
tcf(c_7923,plain,
( pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,sK2(sK3,sK4,sK6)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7877,c_2813]) ).
tcf(c_9287,plain,
! [X0: $i] :
( ~ strictly_less_than(sK6,X0)
| ~ less_than(X0,sK6) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_9314,plain,
( less_than(sK2(sK3,sK4,sK6),sK6)
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| strictly_less_than(sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(superposition,[status(thm)],[c_7923,c_4398]) ).
tcf(c_9628,plain,
! [X0: $i] :
( contains_slb(X0,sK6)
| ~ contains_slb(sK4,sK6)
| ( sK6 != sK6 )
| ( X0 != sK4 ) ),
inference(instantiation,[status(thm)],[c_3399]) ).
tcf(c_9629,plain,
( contains_slb(create_slb,sK6)
| ~ contains_slb(sK4,sK6)
| ( create_slb != sK4 )
| ( sK6 != sK6 ) ),
inference(instantiation,[status(thm)],[c_9628]) ).
tcf(c_10057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(X3,sK6)
| ~ pair_in_list(X1,sK6,X3)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_10905,plain,
! [X0: $i,X1: $i] :
( ( sK4 = create_slb )
| ( triple(X0,update_slb(sK4,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,sK4,X1)) )
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(sK4,findmin_pqp_res(X0))) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_10906,plain,
! [X0: $i,X1: $i] :
( contains_slb(sK4,findmin_pqp_res(X0))
| ( sK4 = create_slb )
| ( triple(X0,update_slb(sK4,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,sK4,X1)) ) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_10907,plain,
! [X0: $i,X1: $i] :
( ( sK4 = create_slb )
| ( findmin_cpq_res(triple(X0,sK4,X1)) = findmin_pqp_res(X0) ) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_19666,plain,
( less_than(sK2(sK3,sK4,sK6),sK6)
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(superposition,[status(thm)],[c_7923,c_4264]) ).
tcf(c_19667,plain,
( less_than(findmin_pqp_res(sK3),sK6)
| less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(superposition,[status(thm)],[c_7467,c_4264]) ).
tcf(c_20841,plain,
~ contains_slb(create_slb,sK6),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_24791,plain,
contains_slb(sK4,sK6),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_25208,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X2,X1)
| pair_in_list(X0,sK0(X0),sK1(X0))
| ~ pair_in_list(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_26081,plain,
( less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ contains_slb(sK4,sK6) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
tcf(c_26097,plain,
( less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26081,c_24791]) ).
tcf(c_47893,plain,
( less_than(findmin_pqp_res(sK3),sK6)
| less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(superposition,[status(thm)],[c_26097,c_25208]) ).
tcf(c_51942,plain,
( ( sK4 = create_slb )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) = findmin_pqp_res(sK3) ) ),
inference(instantiation,[status(thm)],[c_10907]) ).
tcf(c_51945,plain,
( less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),sK6)
| ~ less_than(findmin_pqp_res(sK3),sK6)
| ( sK6 != sK6 )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) != findmin_pqp_res(sK3) ) ),
inference(instantiation,[status(thm)],[c_5050]) ).
tcf(c_57827,plain,
( check_cpq(triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),bad))
| ~ check_cpq(findmin_cpq_eff(triple(sK3,sK4,sK5)))
| ( triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),bad) != findmin_cpq_eff(triple(sK3,sK4,sK5)) ) ),
inference(instantiation,[status(thm)],[c_3173]) ).
tcf(c_57828,plain,
( ( sK4 = create_slb )
| ( triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),bad) = findmin_cpq_eff(triple(sK3,sK4,sK5)) )
| ~ strictly_less_than(findmin_pqp_res(sK3),lookup_slb(sK4,findmin_pqp_res(sK3))) ),
inference(instantiation,[status(thm)],[c_10905]) ).
tcf(c_57829,plain,
( contains_slb(sK4,findmin_pqp_res(sK3))
| ( sK4 = create_slb )
| ( triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),bad) = findmin_cpq_eff(triple(sK3,sK4,sK5)) ) ),
inference(instantiation,[status(thm)],[c_10906]) ).
tcf(c_81999,plain,
! [X0: $i,X1: $i] :
( less_than(sK2(sK3,sK4,sK6),sK6)
| ~ check_cpq(triple(X0,update_slb(sK4,findmin_pqp_res(sK3)),X1))
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,sK2(sK3,sK4,sK6)) ),
inference(instantiation,[status(thm)],[c_10057]) ).
tcf(c_83598,plain,
( ~ strictly_less_than(sK6,sK2(sK3,sK4,sK6))
| ~ less_than(sK2(sK3,sK4,sK6),sK6) ),
inference(instantiation,[status(thm)],[c_9287]) ).
tcf(c_85700,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(findmin_pqp_res(X1),sK6)
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(X1)),sK6,findmin_pqp_res(X1))
| ~ check_cpq(triple(X0,update_slb(sK4,findmin_pqp_res(X1)),X2)) ),
inference(instantiation,[status(thm)],[c_10057]) ).
tcf(c_108208,plain,
( strictly_less_than(sK6,sK2(sK3,sK4,sK6))
| strictly_less_than(sK2(sK3,sK4,sK6),findmin_cpq_res(triple(sK3,sK4,sK5)))
| ~ strictly_less_than(sK6,findmin_cpq_res(triple(sK3,sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_3180]) ).
tcf(c_110099,plain,
! [X0: $i,X1: $i] :
( check_cpq(triple(X0,update_slb(sK4,findmin_pqp_res(sK3)),X1))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_110117,plain,
( less_than(sK2(sK3,sK4,sK6),sK6)
| ~ check_cpq(triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),bad))
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,sK2(sK3,sK4,sK6)) ),
inference(instantiation,[status(thm)],[c_81999]) ).
tcf(c_110386,plain,
! [X0: $i,X1: $i] :
( less_than(findmin_pqp_res(sK3),sK6)
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ check_cpq(triple(X0,update_slb(sK4,findmin_pqp_res(sK3)),X1)) ),
inference(instantiation,[status(thm)],[c_85700]) ).
tcf(c_137772,plain,
sK2(sK3,sK4,sK6) = sK2(sK3,sK4,sK6),
inference(instantiation,[status(thm)],[c_1798]) ).
tcf(c_161802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(X3,sK6)
| ~ pair_in_list(X1,sK6,X3)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_162021,plain,
( pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3))))
| less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6)) ),
inference(global_subsumption_just,[status(thm)],[c_47893,c_94,c_56,c_98,c_109,c_2813,c_3171,c_3672,c_5299,c_9629,c_19667,c_20841,c_51942,c_51945]) ).
tcf(c_162022,plain,
( less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(renaming,[status(thm)],[c_162021]) ).
tcf(c_167850,plain,
! [X0: $i,X1: $i] :
( less_than(findmin_pqp_res(sK3),sK6)
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ check_cpq(triple(X0,update_slb(sK4,findmin_pqp_res(sK3)),X1)) ),
inference(instantiation,[status(thm)],[c_161802]) ).
tcf(c_180854,plain,
( less_than(findmin_pqp_res(sK3),sK6)
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ check_cpq(triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),bad)) ),
inference(instantiation,[status(thm)],[c_167850]) ).
tcf(c_192521,plain,
contains_slb(sK4,sK6),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_193350,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X2,X1)
| pair_in_list(X0,sK0(X0),sK1(X0))
| ~ pair_in_list(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_193366,plain,
! [X0: $i] :
( ~ strictly_less_than(X0,findmin_cpq_res(triple(sK3,sK4,sK5)))
| ~ less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),X0) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_194600,plain,
! [X0: $i,X1: $i] :
( check_cpq(X0)
| ~ check_cpq(findmin_cpq_eff(X1))
| ( X0 != findmin_cpq_eff(X1) ) ),
inference(instantiation,[status(thm)],[c_1802]) ).
tcf(c_194639,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),X1)
| ~ less_than(X0,X2)
| ( X1 != X2 )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1803]) ).
tcf(c_197667,plain,
( pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,sK2(sK3,sK4,sK6))
| ~ contains_slb(sK4,sK6) ),
inference(superposition,[status(thm)],[c_56,c_52]) ).
tcf(c_197716,plain,
( pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,sK2(sK3,sK4,sK6)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197667,c_192521]) ).
tcf(c_206920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(findmin_cpq_eff(X3))
| ( triple(X0,X1,X2) != findmin_cpq_eff(X3) ) ),
inference(instantiation,[status(thm)],[c_194600]) ).
tcf(c_215107,plain,
contains_slb(sK4,sK6),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_215328,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X2,X1)
| pair_in_list(X0,sK0(X0),sK1(X0))
| ~ pair_in_list(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_216159,plain,
( less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ contains_slb(sK4,sK6) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
tcf(c_216175,plain,
( less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_216159,c_215107]) ).
tcf(c_224499,plain,
! [X0: $i,X1: $i] :
( ( sK4 = create_slb )
| ( triple(X0,update_slb(sK4,findmin_pqp_res(X0)),X1) = findmin_cpq_eff(triple(X0,sK4,X1)) )
| ~ contains_slb(sK4,findmin_pqp_res(X0))
| ~ less_than(lookup_slb(sK4,findmin_pqp_res(X0)),findmin_pqp_res(X0)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_225128,plain,
( less_than(sK2(sK3,sK4,sK6),sK6)
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(superposition,[status(thm)],[c_197716,c_193350]) ).
tcf(c_232245,plain,
! [X0: $i,X1: $i] :
( less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),X0)
| ~ less_than(findmin_pqp_res(sK3),X1)
| ( X0 != X1 )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) != findmin_pqp_res(sK3) ) ),
inference(instantiation,[status(thm)],[c_194639]) ).
tcf(c_233708,plain,
( less_than(sK2(sK3,sK4,sK6),sK6)
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(global_subsumption_just,[status(thm)],[c_225128,c_94,c_56,c_98,c_109,c_2813,c_3171,c_3672,c_5299,c_9629,c_19666,c_20841,c_51942,c_51945,c_110099,c_110386]) ).
tcf(c_239436,plain,
! [X0: $i,X1: $i] :
( less_than(findmin_pqp_res(sK3),sK6)
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ check_cpq(triple(X0,update_slb(sK4,findmin_pqp_res(sK3)),X1)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_254846,plain,
! [X0: $i] :
( less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),X0)
| ~ less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| ( X0 != sK2(sK3,sK4,sK6) )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) != findmin_pqp_res(sK3) ) ),
inference(instantiation,[status(thm)],[c_232245]) ).
tcf(c_261766,plain,
! [X0: $i] :
( ( sK4 = create_slb )
| ( triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),X0) = findmin_cpq_eff(triple(sK3,sK4,X0)) )
| ~ contains_slb(sK4,findmin_pqp_res(sK3))
| ~ less_than(lookup_slb(sK4,findmin_pqp_res(sK3)),findmin_pqp_res(sK3)) ),
inference(instantiation,[status(thm)],[c_224499]) ).
tcf(c_272143,plain,
! [X0: $i,X1: $i] :
( less_than(sK1(update_slb(sK4,findmin_pqp_res(sK3))),sK0(update_slb(sK4,findmin_pqp_res(sK3))))
| ~ check_cpq(triple(X0,update_slb(sK4,findmin_pqp_res(sK3)),X1))
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_272183,plain,
( less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),sK2(sK3,sK4,sK6))
| ~ less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| ( sK2(sK3,sK4,sK6) != sK2(sK3,sK4,sK6) )
| ( findmin_cpq_res(triple(sK3,sK4,sK5)) != findmin_pqp_res(sK3) ) ),
inference(instantiation,[status(thm)],[c_254846]) ).
tcf(c_272184,plain,
( ( sK4 = create_slb )
| ( triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),sK5) = findmin_cpq_eff(triple(sK3,sK4,sK5)) )
| ~ contains_slb(sK4,findmin_pqp_res(sK3))
| ~ less_than(lookup_slb(sK4,findmin_pqp_res(sK3)),findmin_pqp_res(sK3)) ),
inference(instantiation,[status(thm)],[c_261766]) ).
tcf(c_272195,plain,
! [X0: $i] :
( check_cpq(triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),X0))
| ~ check_cpq(findmin_cpq_eff(triple(sK3,sK4,X0)))
| ( triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),X0) != findmin_cpq_eff(triple(sK3,sK4,X0)) ) ),
inference(instantiation,[status(thm)],[c_206920]) ).
tcf(c_286411,plain,
( less_than(findmin_pqp_res(sK3),sK6)
| less_than(findmin_pqp_res(sK3),sK2(sK3,sK4,sK6))
| pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(superposition,[status(thm)],[c_216175,c_215328]) ).
tcf(c_305229,plain,
( strictly_less_than(findmin_pqp_res(sK3),lookup_slb(sK4,findmin_pqp_res(sK3)))
| less_than(lookup_slb(sK4,findmin_pqp_res(sK3)),findmin_pqp_res(sK3)) ),
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_309488,plain,
( ~ strictly_less_than(sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3))))
| ~ less_than(sK1(update_slb(sK4,findmin_pqp_res(sK3))),sK0(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_309492,plain,
( ~ strictly_less_than(sK2(sK3,sK4,sK6),findmin_cpq_res(triple(sK3,sK4,sK5)))
| ~ less_than(findmin_cpq_res(triple(sK3,sK4,sK5)),sK2(sK3,sK4,sK6)) ),
inference(instantiation,[status(thm)],[c_193366]) ).
tcf(c_313343,plain,
pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))),
inference(global_subsumption_just,[status(thm)],[c_286411,c_94,c_56,c_98,c_109,c_2813,c_3672,c_5299,c_9629,c_20841,c_51942,c_83598,c_108208,c_137772,c_162022,c_233708,c_272183,c_309492]) ).
tcf(c_314152,plain,
( check_cpq(triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),sK5))
| ~ check_cpq(findmin_cpq_eff(triple(sK3,sK4,sK5)))
| ( triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),sK5) != findmin_cpq_eff(triple(sK3,sK4,sK5)) ) ),
inference(instantiation,[status(thm)],[c_272195]) ).
tcf(c_323616,plain,
( less_than(sK1(update_slb(sK4,findmin_pqp_res(sK3))),sK0(update_slb(sK4,findmin_pqp_res(sK3))))
| ~ check_cpq(triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),sK5))
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK0(update_slb(sK4,findmin_pqp_res(sK3))),sK1(update_slb(sK4,findmin_pqp_res(sK3)))) ),
inference(instantiation,[status(thm)],[c_272143]) ).
tcf(c_323617,plain,
( less_than(findmin_pqp_res(sK3),sK6)
| ~ pair_in_list(update_slb(sK4,findmin_pqp_res(sK3)),sK6,findmin_pqp_res(sK3))
| ~ check_cpq(triple(sK3,update_slb(sK4,findmin_pqp_res(sK3)),sK5)) ),
inference(instantiation,[status(thm)],[c_239436]) ).
tcf(c_324033,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_323616,c_323617,c_314152,c_313343,c_309492,c_309488,c_305229,c_272184,c_272183,c_180854,c_137772,c_110117,c_108208,c_83598,c_57828,c_57829,c_57827,c_51945,c_51942,c_20841,c_9629,c_9314,c_7923,c_7467,c_5299,c_3672,c_3171,c_2813,c_109,c_98,c_56,c_54,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV407+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.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 : Thu Sep 24 19:29:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 127.89/18.00 % SZS status Started for theBenchmark.p
% 127.89/18.00 % SZS status Theorem for theBenchmark.p
% 127.89/18.00
% 127.89/18.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 127.89/18.00
% 127.89/18.00 % ------ iProver source info
% 127.89/18.00
% 127.89/18.00 % git: date: 2026-07-19 20:42:38 +0200
% 127.89/18.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 127.89/18.00 % git: non_committed_changes: false
% 127.89/18.00
% 127.89/18.00 % ------ Parsing...
% 127.89/18.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 127.89/18.00
% 127.89/18.00 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 127.89/18.00
% 127.89/18.00 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 127.89/18.00
% 127.89/18.00 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 127.89/18.00 % ------ Proving...
% 127.89/18.00 % ------ Problem Properties
% 127.89/18.00
% 127.89/18.00 %
% 127.89/18.00 % clauses 39
% 127.89/18.00 % conjectures 3
% 127.89/18.00 % EPR 7
% 127.89/18.00 % Horn 24
% 127.89/18.00 % unary 12
% 127.89/18.00 % binary 15
% 127.89/18.00 % lits 81
% 127.89/18.00 % lits eq 19
% 127.89/18.00 % fd_pure 0
% 127.89/18.00 % fd_pseudo 0
% 127.89/18.00 % fd_cond 4
% 127.89/18.00 % fd_pseudo_cond 4
% 127.89/18.00 % AC symbols 0
% 127.89/18.00
% 127.89/18.00 % ------ Schedule dynamic 5 is on
% 127.89/18.00
% 127.89/18.00 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 127.89/18.00
% 127.89/18.00
% 127.89/18.00 % ------
% 127.89/18.00 % Current options:
% 127.89/18.00 % ------
% 127.89/18.00
% 127.89/18.00
% 127.89/18.00 %
% 127.89/18.00
% 127.89/18.00 % ------ Proving...
% 127.89/18.00 % Proof_search_loop: time out after: 5675 full_loop iterations
% 127.89/18.00
% 127.89/18.00 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 127.89/18.00
% 127.89/18.00
% 127.89/18.00 % ------
% 127.89/18.00 % Current options:
% 127.89/18.00 % ------
% 127.89/18.00
% 127.89/18.00
% 127.89/18.00 %
% 127.89/18.00
% 127.89/18.00 % ------ Proving...
% 127.89/18.00 %
% 127.89/18.00
% 127.89/18.00 % SZS status Theorem for theBenchmark.p
% 127.89/18.00
% 127.89/18.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 127.89/18.01
% 127.89/18.01
%------------------------------------------------------------------------------