TSTP Solution File: KLE022+4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE022+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:31:45 EDT 2023
% Result : Theorem 2.36s 1.20s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 24 unt; 0 def)
% Number of atoms : 118 ( 52 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 107 ( 44 ~; 32 |; 18 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn; 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X3,X4] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f19,conjecture,
! [X3,X4] :
( test(X4)
=> ( leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3)
& leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( test(X4)
=> ( leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3)
& leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4)))) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f23,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f28,plain,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
& leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) ) ),
inference(rectify,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f30,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f37,plain,
? [X0,X1] :
( ( ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
| ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) )
& test(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f42,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f31]) ).
fof(f45,plain,
( ? [X0,X1] :
( ( ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0)
| ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))) )
& test(X1) )
=> ( ( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) )
& test(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
( ( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) )
& test(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f37,f45]) ).
fof(f47,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f48,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f21]) ).
fof(f50,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f54,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f63,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f65,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f70,plain,
test(sK2),
inference(cnf_transformation,[],[f46]) ).
fof(f71,plain,
( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
inference(cnf_transformation,[],[f46]) ).
fof(f72,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f65]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f47]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f48]) ).
cnf(c_52,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[],[f50]) ).
cnf(c_54,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f52]) ).
cnf(c_56,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f54]) ).
cnf(c_60,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_64,plain,
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_68,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_72,negated_conjecture,
( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
inference(cnf_transformation,[],[f71]) ).
cnf(c_73,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f70]) ).
cnf(c_227,plain,
( ~ leq(multiplication(sK1,addition(c(sK2),sK2)),sK1)
| ~ leq(sK1,multiplication(sK1,addition(c(sK2),sK2))) ),
inference(ac_demodulation,[status(thm)],[c_72,c_56,c_56,c_50,c_49]) ).
cnf(c_228,plain,
( ~ leq(multiplication(sK1,addition(sK2,c(sK2))),sK1)
| ~ leq(sK1,multiplication(sK1,addition(sK2,c(sK2)))) ),
inference(theory_normalisation,[status(thm)],[c_227,c_50,c_49]) ).
cnf(c_676,plain,
( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
inference(demodulation,[status(thm)],[c_228,c_56]) ).
cnf(c_718,plain,
leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
cnf(c_735,plain,
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(superposition,[status(thm)],[c_68,c_64]) ).
cnf(c_736,plain,
( ~ test(X0)
| addition(X0,c(X0)) = one ),
inference(theory_normalisation,[status(thm)],[c_735,c_50,c_49]) ).
cnf(c_912,plain,
addition(sK2,c(sK2)) = one,
inference(superposition,[status(thm)],[c_73,c_736]) ).
cnf(c_925,plain,
addition(multiplication(X0,sK2),multiplication(X0,c(sK2))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_912,c_56]) ).
cnf(c_932,plain,
addition(multiplication(X0,sK2),multiplication(X0,c(sK2))) = X0,
inference(light_normalisation,[status(thm)],[c_925,c_54]) ).
cnf(c_933,plain,
~ leq(sK1,sK1),
inference(demodulation,[status(thm)],[c_676,c_932]) ).
cnf(c_934,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_933,c_718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE022+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 12:22:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.36/1.20 % SZS status Started for theBenchmark.p
% 2.36/1.20 % SZS status Theorem for theBenchmark.p
% 2.36/1.20
% 2.36/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.36/1.20
% 2.36/1.20 ------ iProver source info
% 2.36/1.20
% 2.36/1.20 git: date: 2023-05-31 18:12:56 +0000
% 2.36/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.36/1.20 git: non_committed_changes: false
% 2.36/1.20 git: last_make_outside_of_git: false
% 2.36/1.20
% 2.36/1.20 ------ Parsing...
% 2.36/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.36/1.20
% 2.36/1.20 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.36/1.20
% 2.36/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.36/1.20
% 2.36/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.36/1.20 ------ Proving...
% 2.36/1.20 ------ Problem Properties
% 2.36/1.20
% 2.36/1.20
% 2.36/1.20 clauses 25
% 2.36/1.20 conjectures 1
% 2.36/1.20 EPR 2
% 2.36/1.20 Horn 24
% 2.36/1.20 unary 12
% 2.36/1.20 binary 9
% 2.36/1.20 lits 43
% 2.36/1.20 lits eq 22
% 2.36/1.20 fd_pure 0
% 2.36/1.20 fd_pseudo 0
% 2.36/1.20 fd_cond 0
% 2.36/1.20 fd_pseudo_cond 1
% 2.36/1.20 AC symbols 1
% 2.36/1.20
% 2.36/1.20 ------ Schedule dynamic 5 is on
% 2.36/1.20
% 2.36/1.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.36/1.20
% 2.36/1.20
% 2.36/1.20 ------
% 2.36/1.20 Current options:
% 2.36/1.20 ------
% 2.36/1.20
% 2.36/1.20
% 2.36/1.20
% 2.36/1.20
% 2.36/1.20 ------ Proving...
% 2.36/1.20
% 2.36/1.20
% 2.36/1.20 % SZS status Theorem for theBenchmark.p
% 2.36/1.20
% 2.36/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.36/1.20
% 2.36/1.20
%------------------------------------------------------------------------------