TSTP Solution File: KLE027+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : KLE027+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 42.08s 9.07s
% Output : CNFRefutation 42.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 80 ( 45 unt; 0 def)
% Number of atoms : 154 ( 83 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 122 ( 48 ~; 33 |; 27 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 132 ( 2 sgn; 81 !; 20 ?)
% 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
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(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox2/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/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,X5,X6,X7] :
( ( test(X7)
& test(X6) )
=> addition(multiplication(X6,addition(multiplication(X6,X3),multiplication(c(X6),X4))),multiplication(c(X6),X5)) = addition(multiplication(X6,X3),multiplication(c(X6),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X3,X4,X5,X6,X7] :
( ( test(X7)
& test(X6) )
=> addition(multiplication(X6,addition(multiplication(X6,X3),multiplication(c(X6),X4))),multiplication(c(X6),X5)) = addition(multiplication(X6,X3),multiplication(c(X6),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(f24,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f28,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(rectify,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4] :
( addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2))
& test(X4)
& test(X3) ),
inference(ennf_transformation,[],[f28]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4] :
( addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2))
& test(X4)
& test(X3) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f38,f39]) ).
fof(f41,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(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(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f44,plain,
( ? [X0,X1,X2,X3,X4] :
( addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2))
& test(X4)
& test(X3) )
=> ( addition(multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2))),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3))
& test(sK5)
& test(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
( addition(multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2))),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3))
& test(sK5)
& test(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f36,f44]) ).
fof(f46,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f47,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f21]) ).
fof(f48,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f50,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f53,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f57,plain,
! [X0] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f59,plain,
! [X0,X1] :
( zero = multiplication(X0,X1)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f60,plain,
! [X0,X1] :
( zero = multiplication(X1,X0)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f61,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f68,plain,
test(sK4),
inference(cnf_transformation,[],[f45]) ).
fof(f70,plain,
addition(multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2))),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(cnf_transformation,[],[f45]) ).
fof(f71,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f63]) ).
cnf(c_49,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f46]) ).
cnf(c_50,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f47]) ).
cnf(c_51,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[],[f48]) ).
cnf(c_53,plain,
multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f50]) ).
cnf(c_54,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f51]) ).
cnf(c_56,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f53]) ).
cnf(c_59,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f56]) ).
cnf(c_61,plain,
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_63,plain,
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_64,plain,
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_65,plain,
( ~ complement(X0,X1)
| multiplication(X1,X0) = zero ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_67,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(cnf_transformation,[],[f71]) ).
cnf(c_71,negated_conjecture,
addition(multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2))),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(cnf_transformation,[],[f70]) ).
cnf(c_73,negated_conjecture,
test(sK4),
inference(cnf_transformation,[],[f68]) ).
cnf(c_92,negated_conjecture,
addition(multiplication(c(sK4),sK3),multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2)))) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(theory_normalisation,[status(thm)],[c_71,c_50,c_49]) ).
cnf(c_636,plain,
addition(multiplication(c(sK4),sK3),addition(multiplication(sK4,multiplication(sK4,sK1)),multiplication(sK4,multiplication(c(sK4),sK2)))) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(demodulation,[status(thm)],[c_92,c_56]) ).
cnf(c_637,plain,
addition(multiplication(sK4,multiplication(sK4,sK1)),addition(multiplication(c(sK4),sK3),multiplication(sK4,multiplication(c(sK4),sK2)))) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(theory_normalisation,[status(thm)],[c_636,c_50,c_49]) ).
cnf(c_673,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
cnf(c_691,plain,
( ~ test(X0)
| addition(X0,sK0(X0)) = one ),
inference(superposition,[status(thm)],[c_61,c_63]) ).
cnf(c_704,plain,
( ~ test(X0)
| multiplication(X0,c(X0)) = zero ),
inference(superposition,[status(thm)],[c_67,c_64]) ).
cnf(c_713,plain,
( ~ test(X0)
| multiplication(X0,sK0(X0)) = zero ),
inference(superposition,[status(thm)],[c_61,c_65]) ).
cnf(c_745,plain,
addition(sK4,sK0(sK4)) = one,
inference(superposition,[status(thm)],[c_73,c_691]) ).
cnf(c_845,plain,
addition(multiplication(X0,sK4),multiplication(X0,sK0(sK4))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_745,c_56]) ).
cnf(c_849,plain,
addition(multiplication(X0,sK4),multiplication(X0,sK0(sK4))) = X0,
inference(light_normalisation,[status(thm)],[c_845,c_54]) ).
cnf(c_5060,plain,
multiplication(sK4,c(sK4)) = zero,
inference(superposition,[status(thm)],[c_73,c_704]) ).
cnf(c_5111,plain,
multiplication(sK4,multiplication(c(sK4),X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_5060,c_53]) ).
cnf(c_5117,plain,
multiplication(sK4,multiplication(c(sK4),X0)) = zero,
inference(light_normalisation,[status(thm)],[c_5111,c_59]) ).
cnf(c_5118,plain,
addition(multiplication(sK4,multiplication(sK4,sK1)),addition(multiplication(c(sK4),sK3),zero)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(demodulation,[status(thm)],[c_637,c_5117]) ).
cnf(c_5119,plain,
addition(zero,addition(multiplication(sK4,multiplication(sK4,sK1)),multiplication(c(sK4),sK3))) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(theory_normalisation,[status(thm)],[c_5118,c_50,c_49]) ).
cnf(c_5649,plain,
multiplication(sK4,sK0(sK4)) = zero,
inference(superposition,[status(thm)],[c_73,c_713]) ).
cnf(c_8738,plain,
addition(multiplication(sK4,sK4),zero) = sK4,
inference(superposition,[status(thm)],[c_5649,c_849]) ).
cnf(c_8748,plain,
addition(zero,multiplication(sK4,sK4)) = sK4,
inference(theory_normalisation,[status(thm)],[c_8738,c_50,c_49]) ).
cnf(c_8779,plain,
multiplication(sK4,sK4) = sK4,
inference(demodulation,[status(thm)],[c_8748,c_673]) ).
cnf(c_8785,plain,
multiplication(sK4,multiplication(sK4,X0)) = multiplication(sK4,X0),
inference(superposition,[status(thm)],[c_8779,c_53]) ).
cnf(c_163697,plain,
addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(demodulation,[status(thm)],[c_5119,c_673,c_8785]) ).
cnf(c_163698,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_163697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : KLE027+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.15 % Command : run_iprover %s %d THM
% 0.12/0.35 % Computer : n010.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Aug 29 11:10:04 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.17/0.48 Running first-order theorem proving
% 0.17/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 42.08/9.07 % SZS status Started for theBenchmark.p
% 42.08/9.07 % SZS status Theorem for theBenchmark.p
% 42.08/9.07
% 42.08/9.07 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 42.08/9.07
% 42.08/9.07 ------ iProver source info
% 42.08/9.07
% 42.08/9.07 git: date: 2023-05-31 18:12:56 +0000
% 42.08/9.07 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 42.08/9.07 git: non_committed_changes: false
% 42.08/9.07 git: last_make_outside_of_git: false
% 42.08/9.07
% 42.08/9.07 ------ Parsing...
% 42.08/9.07 ------ Clausification by vclausify_rel & Parsing by iProver...
% 42.08/9.07
% 42.08/9.07 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 42.08/9.07
% 42.08/9.07 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 42.08/9.07
% 42.08/9.07 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 42.08/9.07 ------ Proving...
% 42.08/9.07 ------ Problem Properties
% 42.08/9.07
% 42.08/9.07
% 42.08/9.07 clauses 25
% 42.08/9.07 conjectures 3
% 42.08/9.07 EPR 3
% 42.08/9.07 Horn 24
% 42.08/9.07 unary 14
% 42.08/9.07 binary 7
% 42.08/9.07 lits 41
% 42.08/9.07 lits eq 22
% 42.08/9.07 fd_pure 0
% 42.08/9.07 fd_pseudo 0
% 42.08/9.07 fd_cond 0
% 42.08/9.07 fd_pseudo_cond 1
% 42.08/9.07 AC symbols 1
% 42.08/9.07
% 42.08/9.07 ------ Schedule dynamic 5 is on
% 42.08/9.07
% 42.08/9.07 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 42.08/9.07
% 42.08/9.07
% 42.08/9.07 ------
% 42.08/9.07 Current options:
% 42.08/9.07 ------
% 42.08/9.07
% 42.08/9.07
% 42.08/9.07
% 42.08/9.07
% 42.08/9.07 ------ Proving...
% 42.08/9.07
% 42.08/9.07
% 42.08/9.07 % SZS status Theorem for theBenchmark.p
% 42.08/9.07
% 42.08/9.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 42.08/9.07
% 42.08/9.07
%------------------------------------------------------------------------------