TSTP Solution File: KLE026+2 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE026+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.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 05:31:47 EDT 2023
% Result : Theorem 0.50s 1.19s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 39 unt; 0 def)
% Number of atoms : 136 ( 71 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 104 ( 35 ~; 24 |; 31 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn; 66 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
fof(f14,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f19,conjecture,
! [X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> ( multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5)
=> leq(multiplication(X4,X3),multiplication(X3,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X3,X4,X5] :
( ( test(X5)
& test(X4) )
=> ( multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5)
=> leq(multiplication(X4,X3),multiplication(X3,X5)) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f22,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f23,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f28,plain,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
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(f37,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X2)
& test(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X2)
& test(X1) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f41]) ).
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(nnf_transformation,[],[f23]) ).
fof(f44,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,[],[f43]) ).
fof(f46,plain,
( ? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X2)
& test(X1) )
=> ( ~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3))
& multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3)
& test(sK3)
& test(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
( ~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3))
& multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3)
& test(sK3)
& test(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f38,f46]) ).
fof(f48,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f49,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f56,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f59,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f60,plain,
! [X0] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f64,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f71,plain,
test(sK2),
inference(cnf_transformation,[],[f47]) ).
fof(f73,plain,
multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f47]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f48]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f49]) ).
cnf(c_52,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[],[f51]) ).
cnf(c_53,plain,
multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f52]) ).
cnf(c_55,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f54]) ).
cnf(c_57,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f56]) ).
cnf(c_60,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_62,plain,
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_64,plain,
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_72,negated_conjecture,
~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f74]) ).
cnf(c_73,negated_conjecture,
multiplication(multiplication(sK2,sK1),sK3) = multiplication(sK2,sK1),
inference(cnf_transformation,[],[f73]) ).
cnf(c_75,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f71]) ).
cnf(c_219,plain,
multiplication(sK2,multiplication(sK1,sK3)) = multiplication(sK2,sK1),
inference(demodulation,[status(thm)],[c_73,c_53]) ).
cnf(c_249,plain,
( addition(X0,X1) != X1
| multiplication(sK2,sK1) != X0
| multiplication(sK1,sK3) != X1 ),
inference(resolution_lifted,[status(thm)],[c_60,c_72]) ).
cnf(c_250,plain,
addition(multiplication(sK2,sK1),multiplication(sK1,sK3)) != multiplication(sK1,sK3),
inference(unflattening,[status(thm)],[c_249]) ).
cnf(c_935,plain,
addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_943,plain,
addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(superposition,[status(thm)],[c_52,c_935]) ).
cnf(c_991,plain,
( ~ test(X0)
| addition(X0,sK0(X0)) = one ),
inference(superposition,[status(thm)],[c_62,c_64]) ).
cnf(c_1045,plain,
addition(sK2,sK0(sK2)) = one,
inference(superposition,[status(thm)],[c_75,c_991]) ).
cnf(c_1144,plain,
addition(sK2,addition(sK0(sK2),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_1045,c_50]) ).
cnf(c_1268,plain,
addition(sK0(sK2),sK2) = addition(one,sK2),
inference(superposition,[status(thm)],[c_1144,c_943]) ).
cnf(c_1269,plain,
addition(sK2,sK0(sK2)) = addition(one,sK2),
inference(theory_normalisation,[status(thm)],[c_1268,c_50,c_49]) ).
cnf(c_1270,plain,
addition(one,sK2) = one,
inference(light_normalisation,[status(thm)],[c_1269,c_1045]) ).
cnf(c_1409,plain,
addition(multiplication(one,X0),multiplication(sK2,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1270,c_57]) ).
cnf(c_1420,plain,
addition(X0,multiplication(sK2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1409,c_55]) ).
cnf(c_1805,plain,
addition(multiplication(sK1,sK3),multiplication(sK2,sK1)) = multiplication(sK1,sK3),
inference(superposition,[status(thm)],[c_219,c_1420]) ).
cnf(c_1823,plain,
addition(multiplication(sK2,sK1),multiplication(sK1,sK3)) = multiplication(sK1,sK3),
inference(theory_normalisation,[status(thm)],[c_1805,c_50,c_49]) ).
cnf(c_1824,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1823,c_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE026+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 12:08:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.50/1.19 % SZS status Started for theBenchmark.p
% 0.50/1.19 % SZS status Theorem for theBenchmark.p
% 0.50/1.19
% 0.50/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.50/1.19
% 0.50/1.19 ------ iProver source info
% 0.50/1.19
% 0.50/1.19 git: date: 2023-05-31 18:12:56 +0000
% 0.50/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.50/1.19 git: non_committed_changes: false
% 0.50/1.19 git: last_make_outside_of_git: false
% 0.50/1.19
% 0.50/1.19 ------ Parsing...
% 0.50/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.50/1.19
% 0.50/1.19 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 0.50/1.19
% 0.50/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.50/1.19
% 0.50/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.50/1.19 ------ Proving...
% 0.50/1.19 ------ Problem Properties
% 0.50/1.19
% 0.50/1.19
% 0.50/1.19 clauses 26
% 0.50/1.19 conjectures 2
% 0.50/1.19 EPR 3
% 0.50/1.19 Horn 25
% 0.50/1.19 unary 15
% 0.50/1.19 binary 7
% 0.50/1.19 lits 42
% 0.50/1.19 lits eq 23
% 0.50/1.19 fd_pure 0
% 0.50/1.19 fd_pseudo 0
% 0.50/1.19 fd_cond 0
% 0.50/1.19 fd_pseudo_cond 1
% 0.50/1.19 AC symbols 1
% 0.50/1.19
% 0.50/1.19 ------ Schedule dynamic 5 is on
% 0.50/1.19
% 0.50/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.50/1.19
% 0.50/1.19
% 0.50/1.19 ------
% 0.50/1.19 Current options:
% 0.50/1.19 ------
% 0.50/1.19
% 0.50/1.19
% 0.50/1.19
% 0.50/1.19
% 0.50/1.19 ------ Proving...
% 0.50/1.19
% 0.50/1.19
% 0.50/1.19 % SZS status Theorem for theBenchmark.p
% 0.50/1.19
% 0.50/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.65/1.19
% 0.65/1.20
%------------------------------------------------------------------------------