%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV407+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:47:35 PM UTC 2026
% Result : Theorem 9.73s 2.03s
% Output : CNFRefutation 9.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 68
% Syntax : Number of formulae : 297 ( 28 unt; 48 def)
% Number of atoms : 897 ( 99 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1019 ( 419 ~; 488 |; 42 &)
% ( 57 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 57 ( 54 usr; 50 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 570 ( 557 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,V,W] :
( ( less_than(V,W)
& less_than(U,V) )
=> less_than(U,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] : less_than(U,U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] : less_than(bottom,U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ( X = Y
& V = W )
| pair_in_list(U,W,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] : update_slb(create_slb,U) = create_slb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [U,V,W,X] :
( strictly_less_than(X,W)
=> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U,V,W,X,Y] :
( strictly_less_than(X,Y)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,X),X)
& contains_slb(V,X) )
=> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [U,V,W,X] :
( ( ~ contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U,V,W,X] :
( ( strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U,V] : findmin_cpq_res(triple(U,create_slb,V)) = bottom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U,V,W,X] :
( V != create_slb
=> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,lemma,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( pair_in_list(V,X,Y)
=> less_than(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,lemma,
! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [U,V,W] :
( ? [X] :
( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_cpq(triple(U,V,W),X) )
=> ~ check_cpq(findmin_cpq_eff(triple(U,V,W))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [U,V,W] :
( ? [X] :
( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_cpq(triple(U,V,W),X) )
=> ~ check_cpq(findmin_cpq_eff(triple(U,V,W))) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
! [U,W] :
( less_than(U,W)
| ! [V] :
( ~ less_than(V,W)
| ~ less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f50,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f51,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f52,plain,
( ! [U,V] :
( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ! [U,V] :
( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( less_than(X0,X1)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f66,plain,
! [U,V,W,X,Y] :
( ( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f67,plain,
( ! [U,V,W,X,Y] :
( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ! [U,V,W,X,Y] :
( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( X2 != X4
| X1 != X3
| pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f80,plain,
! [X0] : update_slb(create_slb,X0) = create_slb,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f81,plain,
! [U,V,W,X] :
( update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W))
| ~ strictly_less_than(X,W) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
! [W,X] :
( ! [U,V] : update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W))
| ~ strictly_less_than(X,W) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( update_slb(insert_slb(X2,pair(X3,X0)),X1) = insert_slb(update_slb(X2,X1),pair(X3,X1))
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f99,plain,
! [U,V,W,X,Y] :
( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) )
| ~ less_than(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f100,plain,
! [U,V,W,X,Y] :
( ( ( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X,Y] :
( ( ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ! [U,V,W] :
( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4] :
( check_cpq(triple(X2,X3,X4))
| ~ check_cpq(triple(X2,insert_slb(X3,pair(X1,X0)),X4))
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f104,plain,
! [U,V,W,X,Y] :
( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> $false )
| ~ strictly_less_than(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f105,plain,
! [U,V,W,X,Y] :
( ( ( $true
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( $false
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ strictly_less_than(X,Y) ),
inference(NNF_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [X,Y] :
( ( ( $true
| ! [U,V,W] : check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( $false
| ! [U,V,W] : ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ strictly_less_than(X,Y) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
! [X,Y] :
( ! [U,V,W] : ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
| ~ strictly_less_than(X,Y) ),
inference(true_and_false_simplification,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4] :
( ~ check_cpq(triple(X2,insert_slb(X3,pair(X0,X1)),X4))
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [U,V,W,X] :
( ( ~ contains_slb(V,X)
| contains_cpq(triple(U,V,W),X) )
& ( contains_slb(V,X)
| ~ contains_cpq(triple(U,V,W),X) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f110,plain,
( ! [V,X] :
( ~ contains_slb(V,X)
| ! [U,W] : contains_cpq(triple(U,V,W),X) )
& ! [V,X] :
( contains_slb(V,X)
| ! [U,W] : ~ contains_cpq(triple(U,V,W),X) ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f124,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W)
| ~ less_than(lookup_slb(V,X),X)
| ~ contains_slb(V,X) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f125,plain,
! [V,X] :
( ! [U,W] : remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W)
| ~ less_than(lookup_slb(V,X),X)
| ~ contains_slb(V,X) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X2,X0,X3),X1) = triple(remove_pqp(X2,X1),remove_slb(X0,X1),X3)
| ~ less_than(lookup_slb(X0,X1),X1)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f131,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f132,plain,
! [U,V] :
( ! [W] : findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| contains_slb(X0,findmin_pqp_res(X1))
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| ~ strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f135,plain,
! [U,V] :
( ! [W] : findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad)
| ~ strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| ~ strictly_less_than(findmin_pqp_res(X1),lookup_slb(X0,findmin_pqp_res(X1)))
| ~ contains_slb(X0,findmin_pqp_res(X1))
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [U,V,W,X] :
( findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W)
| ~ less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f138,plain,
! [U,V] :
( ! [W] : findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W)
| ~ less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
| ~ contains_slb(V,findmin_pqp_res(U))
| V = create_slb ),
inference(miniscoping,[status(thm)],[f137]) ).
fof(f139,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),X2)
| ~ less_than(lookup_slb(X0,findmin_pqp_res(X1)),findmin_pqp_res(X1))
| ~ contains_slb(X0,findmin_pqp_res(X1))
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1] : findmin_cpq_res(triple(X0,create_slb,X1)) = bottom,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f141,plain,
! [U,V,W,X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f142,plain,
! [V] :
( ! [U,W] : findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U)
| V = create_slb ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f143,plain,
! [X0,X1,X2] :
( findmin_cpq_res(triple(X1,X0,X2)) = findmin_pqp_res(X1)
| X0 = create_slb ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f147,plain,
! [U,V,W] :
( ( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(V,X,Y) )
| check_cpq(triple(U,V,W)) )
& ( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ~ check_cpq(triple(U,V,W)) ) ),
inference(NNF_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
( ! [V] :
( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(V,X,Y) )
| ! [U,W] : check_cpq(triple(U,V,W)) )
& ! [V] :
( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ! [U,W] : ~ check_cpq(triple(U,V,W)) ) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f149,plain,
( ! [V] :
( ( ~ less_than(sK1_skl(V),sK0_skl(V))
& pair_in_list(V,sK0_skl(V),sK1_skl(V)) )
| ! [U,W] : check_cpq(triple(U,V,W)) )
& ! [V] :
( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ! [U,W] : ~ check_cpq(triple(U,V,W)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl(V)),skolemize(Y,sK1_skl(V))],[f148]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4] :
( less_than(X4,X3)
| ~ pair_in_list(X1,X3,X4)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f153,plain,
! [U,V,W,X] :
( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
| ~ strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
| ~ contains_slb(V,X) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f154,plain,
! [U,V,X] :
( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
| ! [W] : ~ strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
| ~ contains_slb(V,X) ),
inference(miniscoping,[status(thm)],[f153]) ).
fof(f155,plain,
! [U,V,X] :
( ( less_than(findmin_pqp_res(U),sK2_skl(X,V,U))
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,sK2_skl(X,V,U)) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
| ! [W] : ~ strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
| ~ contains_slb(V,X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X,V,U))],[f154]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,findmin_pqp_res(X2)),X1,sK2_skl(X1,X0,X2))
| pair_in_list(update_slb(X0,findmin_pqp_res(X2)),X1,findmin_pqp_res(X2))
| ~ strictly_less_than(X1,findmin_cpq_res(triple(X2,X0,X3)))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( less_than(findmin_pqp_res(X2),sK2_skl(X1,X0,X2))
| pair_in_list(update_slb(X0,findmin_pqp_res(X2)),X1,findmin_pqp_res(X2))
| ~ strictly_less_than(X1,findmin_cpq_res(triple(X2,X0,X3)))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f158,plain,
? [U,V,W] :
( check_cpq(findmin_cpq_eff(triple(U,V,W)))
& ? [X] :
( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_cpq(triple(U,V,W),X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f159,plain,
( check_cpq(findmin_cpq_eff(triple(sK3_skl,sK4_skl,sK5_skl)))
& strictly_less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)))
& contains_cpq(triple(sK3_skl,sK4_skl,sK5_skl),sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(U,sK3_skl),skolemize(V,sK4_skl),skolemize(W,sK5_skl),skolemize(X,sK6_skl)],[f158]) ).
fof(f160,plain,
contains_cpq(triple(sK3_skl,sK4_skl,sK5_skl),sK6_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
strictly_less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl))),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f162,plain,
check_cpq(findmin_cpq_eff(triple(sK3_skl,sK4_skl,sK5_skl))),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f163,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f49]) ).
fof(f165,plain,
! [X0,X1,X2] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f71]) ).
fof(f166,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| ~ strictly_less_than(findmin_pqp_res(X1),lookup_slb(X0,findmin_pqp_res(X1)))
| X0 = create_slb ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f133]) ).
fof(f167,plain,
~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),sK6_skl),
inference(resolution,[status(thm)],[f54,f161]) ).
fof(f168,plain,
~ strictly_less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),sK6_skl),
inference(resolution,[status(thm)],[f167,f53]) ).
fof(f170,plain,
( sK4_skl = create_slb
| ~ less_than(findmin_pqp_res(sK3_skl),sK6_skl) ),
inference(paramodulation,[status(thm)],[f143,f167]) ).
fof(f171,plain,
( sK4_skl = create_slb
| strictly_less_than(sK6_skl,findmin_pqp_res(sK3_skl)) ),
inference(paramodulation,[status(thm)],[f143,f161]) ).
fof(f172,definition,
( sQ0_spl
<=> less_than(findmin_pqp_res(sK3_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ0_spl
| ~ less_than(findmin_pqp_res(sK3_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ1_spl
<=> sK4_skl = create_slb ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ1_spl
| sK4_skl = create_slb ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f170,f172,f175]) ).
fof(f179,definition,
( sQ2_spl
<=> strictly_less_than(sK6_skl,findmin_pqp_res(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f171,f179,f175]) ).
fof(f185,plain,
! [X0,X1] :
( ~ sQ1_spl
| findmin_cpq_res(triple(X0,sK4_skl,X1)) = bottom ),
inference(backward_demodulation,[status(thm)],[f176,f140]) ).
fof(f194,plain,
( ~ sQ1_spl
| ~ less_than(bottom,sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f185,f167]) ).
fof(f200,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f56]) ).
fof(f201,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f205,plain,
! [X0,X1,X2] :
( update_slb(insert_slb(create_slb,pair(X2,X0)),X1) = insert_slb(create_slb,pair(X2,X1))
| ~ strictly_less_than(X0,X1) ),
inference(paramodulation,[status(thm)],[f80,f83]) ).
fof(f209,plain,
! [X0] :
( sQ0_spl
| ~ less_than(X0,sK6_skl)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f48,f174]) ).
fof(f211,plain,
! [X0,X1] :
( sQ0_spl
| ~ less_than(X1,X0)
| ~ less_than(findmin_pqp_res(sK3_skl),X1)
| ~ less_than(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f209,f48]) ).
fof(f218,plain,
! [X0] :
( ~ less_than(X0,sK6_skl)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f167,f48]) ).
fof(f219,plain,
less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl))),
inference(resolution,[status(thm)],[f167,f49]) ).
fof(f227,plain,
( sK4_skl = create_slb
| ~ strictly_less_than(findmin_pqp_res(sK3_skl),sK6_skl) ),
inference(paramodulation,[status(thm)],[f143,f168]) ).
fof(f228,definition,
( sQ3_spl
<=> strictly_less_than(findmin_pqp_res(sK3_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f227,f228,f175]) ).
fof(f232,plain,
( sK4_skl = create_slb
| less_than(sK6_skl,findmin_pqp_res(sK3_skl)) ),
inference(paramodulation,[status(thm)],[f143,f219]) ).
fof(f233,definition,
( sQ4_spl
<=> less_than(sK6_skl,findmin_pqp_res(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f232,f233,f175]) ).
fof(f239,plain,
! [X0,X1,X2] :
( sQ0_spl
| ~ less_than(X2,X1)
| ~ less_than(findmin_pqp_res(sK3_skl),X2)
| ~ less_than(X1,X0)
| ~ less_than(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f211,f48]) ).
fof(f240,plain,
! [X0,X1] :
( sQ0_spl
| less_than(X1,findmin_pqp_res(sK3_skl))
| ~ less_than(X1,X0)
| ~ less_than(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f211,f49]) ).
fof(f243,definition,
! [X0] :
( sQ5_spl
<=> ( ~ less_than(findmin_pqp_res(sK3_skl),X0)
| ~ less_than(X0,sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f247,plain,
! [X0,X1] :
( sQ0_spl
| ~ less_than(findmin_pqp_res(sK3_skl),X1)
| ~ less_than(X1,sK6_skl)
| ~ less_than(findmin_pqp_res(sK3_skl),X0)
| ~ less_than(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f240,f211]) ).
fof(f249,plain,
( sQ0_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f247,f243,f172]) ).
fof(f252,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ check_cpq(triple(X4,insert_slb(insert_slb(X5,pair(X0,X1)),pair(X3,X2)),X6))
| ~ less_than(X2,X3)
| ~ strictly_less_than(X0,X1) ),
inference(resolution,[status(thm)],[f108,f102]) ).
fof(f253,plain,
~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),bottom),
inference(resolution,[status(thm)],[f218,f56]) ).
fof(f254,plain,
! [X0,X1] :
( ~ less_than(X1,sK6_skl)
| ~ less_than(X0,X1)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f218,f48]) ).
fof(f255,plain,
! [X0] :
( less_than(sK6_skl,X0)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f218,f49]) ).
fof(f266,plain,
! [X0] :
( create_slb = create_slb
| findmin_pqp_res(X0) = bottom ),
inference(paramodulation,[status(thm)],[f143,f140]) ).
fof(f268,definition,
! [X0] :
( sQ6_spl
<=> findmin_pqp_res(X0) = bottom ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f269,plain,
! [X0] :
( ~ sQ6_spl
| findmin_pqp_res(X0) = bottom ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,definition,
( sQ7_spl
<=> create_slb = create_slb ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f266,f268,f271]) ).
fof(f285,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ less_than(bottom,sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f269,f174]) ).
fof(f298,plain,
( sQ0_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f56]) ).
fof(f299,plain,
( sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f305,plain,
! [X0,X1,X2,X3,X4] :
( less_than(X3,X2)
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) ),
inference(resolution,[status(thm)],[f165,f150]) ).
fof(f308,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ check_cpq(triple(X2,insert_slb(insert_slb(X3,pair(X0,X1)),pair(X4,X5)),X6))
| ~ strictly_less_than(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f252,f305]) ).
fof(f324,plain,
! [X0] :
( ~ less_than(X0,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f253,f48]) ).
fof(f326,plain,
~ strictly_less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),bottom),
inference(resolution,[status(thm)],[f253,f53]) ).
fof(f337,plain,
( sK4_skl = create_slb
| ~ strictly_less_than(findmin_pqp_res(sK3_skl),bottom) ),
inference(paramodulation,[status(thm)],[f143,f326]) ).
fof(f338,plain,
( sK4_skl = create_slb
| ~ less_than(findmin_pqp_res(sK3_skl),bottom) ),
inference(paramodulation,[status(thm)],[f143,f253]) ).
fof(f346,definition,
( sQ8_spl
<=> strictly_less_than(findmin_pqp_res(sK3_skl),bottom) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( sQ1_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f337,f346,f175]) ).
fof(f350,definition,
( sQ9_spl
<=> less_than(findmin_pqp_res(sK3_skl),bottom) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ9_spl
| ~ less_than(findmin_pqp_res(sK3_skl),bottom) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( sQ1_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f338,f350,f175]) ).
fof(f360,plain,
! [X0] :
( sQ9_spl
| ~ less_than(X0,bottom)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f352,f48]) ).
fof(f364,plain,
! [X0,X1] :
( sQ9_spl
| ~ less_than(X1,bottom)
| ~ less_than(X0,X1)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f360,f48]) ).
fof(f375,plain,
! [X0,X1,X2] :
( sQ9_spl
| ~ less_than(X2,bottom)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f364,f48]) ).
fof(f383,definition,
! [X0] :
( sQ10_spl
<=> ( ~ less_than(X0,bottom)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f389,definition,
( sQ11_spl
<=> less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f401,plain,
! [X0,X1,X2,X3] :
( findmin_cpq_eff(triple(X1,X0,X3)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),X3)
| ~ less_than(lookup_slb(X0,findmin_pqp_res(X1)),findmin_pqp_res(X1))
| X0 = create_slb
| findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| X0 = create_slb ),
inference(resolution,[status(thm)],[f133,f139]) ).
fof(f406,plain,
! [X0,X1,X2,X3] :
( findmin_cpq_eff(triple(X1,X0,X3)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),X3)
| ~ less_than(lookup_slb(X0,findmin_pqp_res(X1)),findmin_pqp_res(X1))
| findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| X0 = create_slb ),
inference(duplicate_literals_removal,[status(thm)],[f401]) ).
fof(f433,plain,
( ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),sK6_skl)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),sK6_skl) ),
inference(resolution,[status(thm)],[f255,f218]) ).
fof(f434,definition,
( sQ13_spl
<=> less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),bottom) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f440,plain,
~ sQ11_spl,
inference(split_clause,[status(thm)],[f433,f389]) ).
fof(f447,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X1)
| ~ less_than(X0,bottom) ),
inference(resolution,[status(thm)],[f324,f48]) ).
fof(f448,plain,
! [X0] :
( less_than(X0,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)))
| ~ less_than(X0,bottom) ),
inference(resolution,[status(thm)],[f324,f49]) ).
fof(f450,plain,
! [X0] :
( ~ strictly_less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0)
| ~ less_than(X0,bottom) ),
inference(resolution,[status(thm)],[f324,f53]) ).
fof(f451,plain,
! [X0] :
( sK4_skl = create_slb
| ~ less_than(X0,bottom)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(paramodulation,[status(thm)],[f143,f324]) ).
fof(f452,definition,
! [X0] :
( sQ14_spl
<=> ( ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0)
| ~ less_than(X0,sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f451,f383,f175]) ).
fof(f459,plain,
( ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),bottom) ),
inference(resolution,[status(thm)],[f448,f324]) ).
fof(f460,plain,
! [X0] :
( sK4_skl = create_slb
| less_than(X0,findmin_pqp_res(sK3_skl))
| ~ less_than(X0,bottom) ),
inference(paramodulation,[status(thm)],[f143,f448]) ).
fof(f462,plain,
~ sQ13_spl,
inference(split_clause,[status(thm)],[f459,f434]) ).
fof(f463,definition,
! [X0] :
( sQ15_spl
<=> ( less_than(X0,findmin_pqp_res(sK3_skl))
| ~ less_than(X0,bottom) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f464,plain,
! [X0] :
( ~ sQ15_spl
| less_than(X0,findmin_pqp_res(sK3_skl))
| ~ less_than(X0,bottom) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f460,f463,f175]) ).
fof(f493,plain,
! [X0] :
( sK4_skl = create_slb
| ~ strictly_less_than(findmin_pqp_res(sK3_skl),X0)
| ~ less_than(X0,bottom) ),
inference(paramodulation,[status(thm)],[f143,f450]) ).
fof(f494,definition,
! [X0] :
( sQ16_spl
<=> ( ~ strictly_less_than(findmin_pqp_res(sK3_skl),X0)
| ~ less_than(X0,bottom) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ1_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f493,f494,f175]) ).
fof(f503,plain,
! [X0,X1,X2] :
( sQ0_spl
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(findmin_pqp_res(sK3_skl),X2)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f239,f49]) ).
fof(f506,definition,
! [X0,X1] :
( sQ17_spl
<=> ( ~ less_than(X1,X0)
| ~ less_than(findmin_pqp_res(sK3_skl),X1)
| ~ less_than(X0,sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f514,plain,
! [X0,X1,X2,X3] :
( sQ9_spl
| ~ less_than(X3,bottom)
| ~ less_than(X2,X3)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f375,f48]) ).
fof(f524,plain,
! [X0,X1] :
( less_than(sK6_skl,X1)
| ~ less_than(X0,X1)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f254,f49]) ).
fof(f536,plain,
! [X0,X1,X2,X3] :
( sQ0_spl
| ~ less_than(X3,X2)
| ~ less_than(findmin_pqp_res(sK3_skl),X3)
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f503,f48]) ).
fof(f537,plain,
! [X0,X1,X2] :
( sQ0_spl
| less_than(X2,findmin_pqp_res(sK3_skl))
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f503,f49]) ).
fof(f540,definition,
! [X0,X1] :
( sQ18_spl
<=> ( less_than(sK6_skl,X1)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f544,definition,
! [X0,X1] :
( sQ19_spl
<=> ( less_than(sK6_skl,X1)
| ~ less_than(findmin_pqp_res(sK3_skl),X0)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f552,plain,
! [X0,X1,X2,X3] :
( sQ0_spl
| less_than(sK6_skl,X3)
| ~ less_than(findmin_pqp_res(sK3_skl),X2)
| ~ less_than(X2,X3)
| less_than(sK6_skl,X1)
| ~ less_than(findmin_pqp_res(sK3_skl),X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f537,f503]) ).
fof(f556,plain,
( sQ0_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f552,f544,f172]) ).
fof(f569,plain,
! [X0,X1,X2] :
( ~ less_than(X2,bottom)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f447,f48]) ).
fof(f576,plain,
! [X0,X1,X2] :
( sQ9_spl
| ~ less_than(X2,sK6_skl)
| ~ less_than(X1,X2)
| ~ less_than(findmin_pqp_res(sK3_skl),X1)
| ~ less_than(X0,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f524,f375]) ).
fof(f579,plain,
! [X0,X1] :
( ~ less_than(X1,sK6_skl)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X1)
| ~ less_than(X0,sK6_skl)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f524,f254]) ).
fof(f584,definition,
! [X0] :
( sQ21_spl
<=> ( ~ less_than(X0,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( sQ9_spl
| sQ17_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f576,f584,f506,f350]) ).
fof(f591,plain,
sQ14_spl,
inference(split_clause,[status(thm)],[f579,f452]) ).
fof(f595,plain,
! [X0,X1,X2] :
( less_than(lookup_slb(X0,findmin_pqp_res(X1)),findmin_pqp_res(X1))
| findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| X0 = create_slb ),
inference(resolution,[status(thm)],[f166,f163]) ).
fof(f597,plain,
! [X0,X1,X2,X3] :
( findmin_cpq_eff(triple(X1,X0,X3)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),X3)
| findmin_cpq_eff(triple(X1,X0,X2)) = triple(X1,update_slb(X0,findmin_pqp_res(X1)),bad)
| X0 = create_slb ),
inference(backward_subsumption_resolution,[status(thm)],[f406,f595]) ).
fof(f599,plain,
! [X0] : update_slb(insert_slb(create_slb,pair(X0,sK6_skl)),findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl))) = insert_slb(create_slb,pair(X0,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)))),
inference(resolution,[status(thm)],[f205,f161]) ).
fof(f663,definition,
! [X0,X1,X2] :
( sQ22_spl
<=> ( ~ less_than(X1,sK6_skl)
| ~ less_than(X2,X0)
| ~ less_than(findmin_pqp_res(sK3_skl),X2)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f669,plain,
! [X0,X1,X2,X3] :
( sQ9_spl
| ~ less_than(X3,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X3)
| ~ less_than(X2,sK6_skl)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f514,f524]) ).
fof(f677,plain,
( sQ9_spl
| sQ21_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f669,f663,f584,f350]) ).
fof(f687,plain,
! [X0,X1,X2,X3] :
( sQ0_spl
| less_than(X3,findmin_pqp_res(sK3_skl))
| ~ less_than(X3,X2)
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f536,f49]) ).
fof(f690,definition,
! [X0,X1,X2] :
( sQ23_spl
<=> ( ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X2)
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f694,definition,
! [X0,X1,X2] :
( sQ24_spl
<=> ( ~ less_than(findmin_pqp_res(sK3_skl),X2)
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f707,plain,
! [X0,X1,X2,X3,X4] : ~ check_cpq(triple(X0,insert_slb(insert_slb(X1,pair(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)))),pair(X2,X3)),X4)),
inference(resolution,[status(thm)],[f308,f161]) ).
fof(f783,plain,
! [X0,X1,X2,X3,X4,X5] :
( sQ0_spl
| ~ less_than(findmin_pqp_res(sK3_skl),X5)
| less_than(sK6_skl,X4)
| ~ less_than(X5,X3)
| ~ less_than(X3,X4)
| ~ less_than(findmin_pqp_res(sK3_skl),X2)
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ),
inference(resolution,[status(thm)],[f687,f536]) ).
fof(f788,plain,
( sQ0_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f783,f694,f172]) ).
fof(f808,plain,
( pair_in_list(update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),sK6_skl,sK2_skl(sK6_skl,sK4_skl,sK3_skl))
| pair_in_list(update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),sK6_skl,findmin_pqp_res(sK3_skl))
| ~ contains_slb(sK4_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f156,f161]) ).
fof(f813,definition,
( sQ25_spl
<=> contains_slb(sK4_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f814,plain,
( ~ sQ25_spl
| contains_slb(sK4_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f813]) ).
fof(f815,plain,
( sQ25_spl
| ~ contains_slb(sK4_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f813]) ).
fof(f816,definition,
( sQ26_spl
<=> pair_in_list(update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),sK6_skl,findmin_pqp_res(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f817,plain,
( ~ sQ26_spl
| pair_in_list(update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),sK6_skl,findmin_pqp_res(sK3_skl)) ),
inference(component_clause,[status(thm)],[f816]) ).
fof(f819,definition,
( sQ27_spl
<=> pair_in_list(update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),sK6_skl,sK2_skl(sK6_skl,sK4_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f820,plain,
( ~ sQ27_spl
| pair_in_list(update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),sK6_skl,sK2_skl(sK6_skl,sK4_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f819]) ).
fof(f822,plain,
( sQ27_spl
| sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f808,f813,f816,f819]) ).
fof(f849,plain,
! [X0,X1] :
( ~ sQ27_spl
| less_than(sK2_skl(sK6_skl,sK4_skl,sK3_skl),sK6_skl)
| ~ check_cpq(triple(X0,update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),X1)) ),
inference(resolution,[status(thm)],[f820,f150]) ).
fof(f850,definition,
! [X0,X1] :
( sQ28_spl
<=> ~ check_cpq(triple(X0,update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),X1)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f851,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ check_cpq(triple(X0,update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),X1)) ),
inference(component_clause,[status(thm)],[f850]) ).
fof(f853,definition,
( sQ29_spl
<=> less_than(sK2_skl(sK6_skl,sK4_skl,sK3_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f854,plain,
( ~ sQ29_spl
| less_than(sK2_skl(sK6_skl,sK4_skl,sK3_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f853]) ).
fof(f856,plain,
( ~ sQ27_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f849,f850,f853,f819]) ).
fof(f860,plain,
! [X0] :
( sQ0_spl
| ~ sQ29_spl
| ~ less_than(X0,sK2_skl(sK6_skl,sK4_skl,sK3_skl))
| ~ less_than(findmin_pqp_res(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f854,f211]) ).
fof(f867,plain,
! [X0,X1] :
( ~ sQ26_spl
| less_than(findmin_pqp_res(sK3_skl),sK6_skl)
| ~ check_cpq(triple(X0,update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),X1)) ),
inference(resolution,[status(thm)],[f817,f150]) ).
fof(f868,plain,
( ~ sQ26_spl
| sQ0_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f867,f850,f172,f816]) ).
fof(f871,plain,
! [X0,X1] :
( sQ25_spl
| ~ contains_cpq(triple(X0,sK4_skl,X1),sK6_skl) ),
inference(resolution,[status(thm)],[f815,f111]) ).
fof(f872,plain,
( sQ25_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f160,f871]) ).
fof(f873,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f872]) ).
fof(f874,plain,
! [X0,X1] :
( ~ sQ25_spl
| remove_cpq(triple(X0,sK4_skl,X1),sK6_skl) = triple(remove_pqp(X0,sK6_skl),remove_slb(sK4_skl,sK6_skl),X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),sK6_skl) ),
inference(resolution,[status(thm)],[f814,f126]) ).
fof(f876,definition,
( sQ30_spl
<=> less_than(lookup_slb(sK4_skl,sK6_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f878,plain,
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f876]) ).
fof(f879,definition,
! [X0,X1] :
( sQ31_spl
<=> remove_cpq(triple(X0,sK4_skl,X1),sK6_skl) = triple(remove_pqp(X0,sK6_skl),remove_slb(sK4_skl,sK6_skl),X1) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( ~ sQ25_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f874,f876,f879,f813]) ).
fof(f885,plain,
! [X0] :
( sQ30_spl
| ~ less_than(X0,sK6_skl)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f878,f48]) ).
fof(f893,plain,
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),bottom) ),
inference(resolution,[status(thm)],[f885,f56]) ).
fof(f897,plain,
! [X0] :
( sQ30_spl
| less_than(sK6_skl,X0)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f885,f49]) ).
fof(f905,plain,
! [X0] :
( sQ30_spl
| ~ less_than(X0,bottom)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f893,f48]) ).
fof(f909,plain,
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),bottom)
| less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f897,f448]) ).
fof(f917,plain,
! [X0,X1] :
( sQ30_spl
| ~ less_than(X1,X0)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X1)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f897,f48]) ).
fof(f918,plain,
! [X0] :
( sQ30_spl
| less_than(X0,lookup_slb(sK4_skl,sK6_skl))
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f897,f49]) ).
fof(f921,definition,
( sQ32_spl
<=> less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f924,definition,
( sQ33_spl
<=> less_than(lookup_slb(sK4_skl,sK6_skl),bottom) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( sQ30_spl
| ~ sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f909,f921,f924,f876]) ).
fof(f928,definition,
! [X0,X1,X2] :
( sQ34_spl
<=> ( ~ less_than(lookup_slb(sK4_skl,sK6_skl),X2)
| less_than(sK6_skl,X1)
| ~ less_than(X2,X0)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f932,definition,
! [X0,X1] :
( sQ35_spl
<=> ( less_than(sK6_skl,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0)
| ~ less_than(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f937,definition,
! [X0] :
( sQ36_spl
<=> ( ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0)
| ~ less_than(X0,sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f949,plain,
! [X0,X1] :
( sQ30_spl
| ~ less_than(X1,bottom)
| ~ less_than(X0,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f905,f48]) ).
fof(f971,plain,
( sQ30_spl
| less_than(sK6_skl,lookup_slb(sK4_skl,sK6_skl))
| less_than(sK6_skl,lookup_slb(sK4_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f918,f897]) ).
fof(f977,definition,
( sQ39_spl
<=> less_than(sK6_skl,lookup_slb(sK4_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f980,plain,
( sQ30_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f971,f977,f876]) ).
fof(f1004,plain,
! [X0] :
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f917,f448]) ).
fof(f1005,plain,
! [X0,X1,X2,X3] :
( sQ0_spl
| sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X3)
| less_than(sK6_skl,X2)
| ~ less_than(X3,X1)
| ~ less_than(X1,X2)
| ~ less_than(findmin_pqp_res(sK3_skl),X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f917,f687]) ).
fof(f1007,plain,
! [X0] :
( ~ sQ15_spl
| sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),bottom)
| ~ less_than(findmin_pqp_res(sK3_skl),X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f917,f464]) ).
fof(f1012,plain,
! [X0,X1,X2] :
( sQ30_spl
| ~ less_than(X2,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X2)
| ~ less_than(X1,X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f917,f48]) ).
fof(f1013,plain,
! [X0,X1] :
( sQ30_spl
| less_than(X1,lookup_slb(sK4_skl,sK6_skl))
| ~ less_than(X1,X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f917,f49]) ).
fof(f1016,definition,
! [X0] :
( sQ40_spl
<=> ( ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0)
| less_than(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1020,definition,
! [X0] :
( sQ41_spl
<=> ( ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0)
| less_than(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1023,plain,
( sQ30_spl
| ~ sQ33_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1004,f1020,f924,f876]) ).
fof(f1024,definition,
! [X0] :
( sQ42_spl
<=> ( ~ less_than(findmin_pqp_res(sK3_skl),X0)
| less_than(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1027,plain,
( sQ0_spl
| sQ30_spl
| sQ34_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1005,f1024,f928,f876,f172]) ).
fof(f1029,plain,
( ~ sQ15_spl
| sQ30_spl
| ~ sQ33_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1007,f1024,f924,f876,f463]) ).
fof(f1053,plain,
! [X0,X1] :
( sQ30_spl
| ~ less_than(X1,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X1)
| ~ less_than(X0,sK6_skl)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f949,f524]) ).
fof(f1059,plain,
! [X0,X1,X2] :
( sQ30_spl
| ~ less_than(X2,bottom)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f949,f48]) ).
fof(f1063,plain,
( sQ30_spl
| sQ21_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f1053,f937,f584,f876]) ).
fof(f1067,plain,
! [X0,X1] :
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X1)
| less_than(sK6_skl,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f1013,f917]) ).
fof(f1074,plain,
( sQ30_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1067,f1016,f876]) ).
fof(f1141,definition,
! [X0,X1] :
( sQ46_spl
<=> ( ~ less_than(X1,sK6_skl)
| ~ less_than(X0,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1149,plain,
! [X0,X1] :
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X1)
| ~ less_than(X1,X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f1012,f448]) ).
fof(f1157,plain,
! [X0,X1,X2,X3] :
( sQ30_spl
| ~ less_than(X3,X2)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X3)
| ~ less_than(X2,X1)
| ~ less_than(X1,X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f1012,f48]) ).
fof(f1158,plain,
! [X0,X1,X2] :
( sQ30_spl
| less_than(X2,lookup_slb(sK4_skl,sK6_skl))
| ~ less_than(X2,X1)
| ~ less_than(X1,X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f1012,f49]) ).
fof(f1163,plain,
( sQ30_spl
| ~ sQ33_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f1149,f540,f924,f876]) ).
fof(f1169,plain,
! [X0,X1,X2] :
( sQ30_spl
| ~ less_than(X2,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X2)
| ~ less_than(X1,sK6_skl)
| ~ less_than(X0,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f1059,f524]) ).
fof(f1175,plain,
! [X0,X1,X2,X3] :
( sQ30_spl
| ~ less_than(X3,bottom)
| ~ less_than(X2,X3)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f1059,f48]) ).
fof(f1179,plain,
( sQ30_spl
| sQ21_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f1169,f1141,f584,f876]) ).
fof(f1183,plain,
! [X0] :
( sK4_skl = create_slb
| update_slb(insert_slb(create_slb,pair(X0,sK6_skl)),findmin_pqp_res(sK3_skl)) = insert_slb(create_slb,pair(X0,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)))) ),
inference(paramodulation,[status(thm)],[f143,f599]) ).
fof(f1185,definition,
! [X0] :
( sQ47_spl
<=> update_slb(insert_slb(create_slb,pair(X0,sK6_skl)),findmin_pqp_res(sK3_skl)) = insert_slb(create_slb,pair(X0,findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1188,plain,
( sQ1_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f1183,f1185,f175]) ).
fof(f1196,plain,
! [X0,X1,X2,X3] :
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X3)
| ~ less_than(X3,X2)
| less_than(sK6_skl,X2)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X1)
| ~ less_than(X1,X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f1158,f1012]) ).
fof(f1204,plain,
( sQ30_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1196,f932,f876]) ).
fof(f1231,definition,
! [X0,X1] :
( sQ48_spl
<=> ( ~ less_than(X1,sK6_skl)
| ~ less_than(X0,X1)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1237,plain,
! [X0,X1,X2] :
( ~ less_than(X2,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X2)
| ~ less_than(X1,sK6_skl)
| ~ less_than(X0,X1)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X0) ),
inference(resolution,[status(thm)],[f569,f524]) ).
fof(f1247,plain,
( sQ21_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f1237,f1231,f584]) ).
fof(f1305,definition,
! [X0] :
( sQ53_spl
<=> ~ check_cpq(findmin_cpq_eff(triple(sK3_skl,sK4_skl,X0))) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
! [X0] :
( ~ sQ53_spl
| ~ check_cpq(findmin_cpq_eff(triple(sK3_skl,sK4_skl,X0))) ),
inference(component_clause,[status(thm)],[f1305]) ).
fof(f1357,plain,
! [X0] :
( sQ0_spl
| ~ sQ29_spl
| pair_in_list(update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),sK6_skl,findmin_pqp_res(sK3_skl))
| ~ strictly_less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,X0)))
| ~ contains_slb(sK4_skl,sK6_skl)
| ~ less_than(findmin_pqp_res(sK3_skl),findmin_pqp_res(sK3_skl)) ),
inference(resolution,[status(thm)],[f860,f157]) ).
fof(f1368,definition,
( sQ61_spl
<=> less_than(findmin_pqp_res(sK3_skl),findmin_pqp_res(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1370,plain,
( sQ61_spl
| ~ less_than(findmin_pqp_res(sK3_skl),findmin_pqp_res(sK3_skl)) ),
inference(component_clause,[status(thm)],[f1368]) ).
fof(f1371,definition,
! [X0] :
( sQ62_spl
<=> ~ strictly_less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,X0))) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1372,plain,
! [X0] :
( ~ sQ62_spl
| ~ strictly_less_than(sK6_skl,findmin_cpq_res(triple(sK3_skl,sK4_skl,X0))) ),
inference(component_clause,[status(thm)],[f1371]) ).
fof(f1374,plain,
( sQ0_spl
| ~ sQ29_spl
| sQ26_spl
| sQ62_spl
| ~ sQ25_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f1357,f1368,f813,f1371,f816,f853,f172]) ).
fof(f1466,definition,
! [X0,X1,X2] :
( sQ66_spl
<=> ( ~ less_than(X2,sK6_skl)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1475,plain,
! [X0,X1,X2] :
( sQ30_spl
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X2)
| ~ less_than(X2,X1)
| ~ less_than(X1,X0)
| less_than(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f1157,f448]) ).
fof(f1490,plain,
( sQ30_spl
| ~ sQ33_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1475,f690,f924,f876]) ).
fof(f1496,plain,
! [X0,X1,X2,X3] :
( sQ30_spl
| ~ less_than(X3,bottom)
| ~ less_than(findmin_cpq_res(triple(sK3_skl,sK4_skl,sK5_skl)),X3)
| ~ less_than(X2,sK6_skl)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| ~ less_than(lookup_slb(sK4_skl,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f1175,f524]) ).
fof(f1506,plain,
( sQ30_spl
| sQ21_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1496,f1466,f584,f876]) ).
fof(f1540,plain,
! [X0,X1,X2,X3,X4] :
( sK4_skl = create_slb
| ~ check_cpq(triple(X0,insert_slb(insert_slb(X1,pair(sK6_skl,findmin_pqp_res(sK3_skl))),pair(X2,X3)),X4)) ),
inference(paramodulation,[status(thm)],[f143,f707]) ).
fof(f1541,definition,
! [X0,X1,X2,X3,X4] :
( sQ67_spl
<=> ~ check_cpq(triple(X0,insert_slb(insert_slb(X1,pair(sK6_skl,findmin_pqp_res(sK3_skl))),pair(X2,X3)),X4)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1544,plain,
( sQ1_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1540,f1541,f175]) ).
fof(f1812,plain,
! [X0,X1] :
( ~ sQ28_spl
| findmin_cpq_eff(triple(sK3_skl,sK4_skl,X1)) = triple(sK3_skl,update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),bad)
| sK4_skl = create_slb
| ~ check_cpq(findmin_cpq_eff(triple(sK3_skl,sK4_skl,X0))) ),
inference(paramodulation,[status(thm)],[f597,f851]) ).
fof(f1848,definition,
! [X3] :
( sQ80_spl
<=> findmin_cpq_eff(triple(sK3_skl,sK4_skl,X3)) = triple(sK3_skl,update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),bad) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1849,plain,
! [X0] :
( ~ sQ80_spl
| findmin_cpq_eff(triple(sK3_skl,sK4_skl,X0)) = triple(sK3_skl,update_slb(sK4_skl,findmin_pqp_res(sK3_skl)),bad) ),
inference(component_clause,[status(thm)],[f1848]) ).
fof(f1853,plain,
( ~ sQ28_spl
| sQ80_spl
| sQ1_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f1812,f1305,f175,f1848,f850]) ).
fof(f1899,plain,
! [X0] :
( ~ sQ80_spl
| ~ sQ28_spl
| ~ check_cpq(findmin_cpq_eff(triple(sK3_skl,sK4_skl,X0))) ),
inference(paramodulation,[status(thm)],[f1849,f851]) ).
fof(f1943,plain,
( ~ sQ80_spl
| ~ sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f162,f1899]) ).
fof(f2004,plain,
( ~ sQ80_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f1943]) ).
fof(f2005,plain,
( ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f1306]) ).
fof(f2006,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f2005]) ).
fof(f2007,plain,
( sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1370,f50]) ).
fof(f2008,plain,
sQ61_spl,
inference(contradiction_clause,[status(thm)],[f2007]) ).
fof(f2009,plain,
( ~ sQ62_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f161,f1372]) ).
fof(f2010,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f2009]) ).
fof(f2011,plain,
$false,
inference(sat_refutation,[status(thm)],[f178,f182,f201,f231,f236,f249,f274,f299,f349,f353,f440,f457,f462,f466,f497,f556,f588,f591,f677,f788,f822,f856,f868,f873,f882,f927,f980,f1023,f1027,f1029,f1063,f1074,f1163,f1179,f1188,f1204,f1247,f1374,f1490,f1506,f1544,f1853,f2004,f2006,f2008,f2010]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV407+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:43:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 9.73/2.03 % Refutation found
% 9.73/2.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.73/2.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.73/2.08 % Elapsed time: 1.710783 seconds
% 9.73/2.08 % CPU time: 12.311932 seconds
% 9.73/2.08 % Total memory used: 195.864 MB
% 9.73/2.08 % Net memory used: 182.728 MB
%------------------------------------------------------------------------------