TSTP Solution File: KLE007+4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 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 : Wed Aug 31 17:28:43 EDT 2022
% Result : Theorem 0.19s 0.57s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 32 unt; 0 def)
% Number of atoms : 140 ( 58 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 125 ( 48 ~; 34 |; 30 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 57 ( 49 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f174,plain,
$false,
inference(subsumption_resolution,[],[f173,f84]) ).
fof(f84,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f173,plain,
one != addition(one,one),
inference(resolution,[],[f170,f82]) ).
fof(f82,plain,
! [X0,X1] :
( leq(X1,X0)
| addition(X1,X0) != X0 ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( leq(X1,X0)
| addition(X1,X0) != X0 ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X1,X0] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X0] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X1,X0] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f170,plain,
~ leq(one,one),
inference(duplicate_literal_removal,[],[f169]) ).
fof(f169,plain,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(forward_demodulation,[],[f168,f165]) ).
fof(f165,plain,
one = sF8,
inference(backward_demodulation,[],[f137,f161]) ).
fof(f161,plain,
one = addition(sK1,sF6),
inference(superposition,[],[f122,f76]) ).
fof(f76,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f122,plain,
one = addition(sF6,sK1),
inference(resolution,[],[f69,f99]) ).
fof(f99,plain,
complement(sK1,sF6),
inference(subsumption_resolution,[],[f97,f65]) ).
fof(f65,plain,
test(sK1),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
( test(sK1)
& test(sK0)
& ( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
| ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f45,f46]) ).
fof(f46,plain,
( ? [X0,X1] :
( test(X1)
& test(X0)
& ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
| ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) )
=> ( test(sK1)
& test(sK0)
& ( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
| ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
| ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) ),
inference(rectify,[],[f35]) ).
fof(f35,plain,
? [X1,X0] :
( test(X0)
& test(X1)
& ( ~ leq(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))),one)
| ~ leq(one,addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0)))) ) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
? [X1,X0] :
( ( ~ leq(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))),one)
| ~ leq(one,addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0)))) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
~ ! [X1,X0] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))))
& leq(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X1,c(X1)),c(X0))),one) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X4,X3] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one)
& leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4)))) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X4,X3] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one)
& leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f97,plain,
( ~ test(sK1)
| complement(sK1,sF6) ),
inference(superposition,[],[f86,f90]) ).
fof(f90,plain,
sF6 = c(sK1),
introduced(function_definition,[]) ).
fof(f86,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ( ( complement(X0,X1)
| c(X0) != X1 )
& ( c(X0) = X1
| ~ complement(X0,X1) ) )
| ~ test(X0) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X1,X0] :
( ( ( complement(X1,X0)
| c(X1) != X0 )
& ( c(X1) = X0
| ~ complement(X1,X0) ) )
| ~ test(X1) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X1,X0] :
( ( complement(X1,X0)
<=> c(X1) = X0 )
| ~ test(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( test(X1)
=> ( complement(X1,X0)
<=> c(X1) = X0 ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X4,X3] :
( test(X3)
=> ( complement(X3,X4)
<=> c(X3) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f69,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ( ( addition(X1,X0) = one
& zero = multiplication(X0,X1)
& zero = multiplication(X1,X0) )
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| addition(X1,X0) != one
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0) ) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ( ( addition(X1,X0) = one
& zero = multiplication(X0,X1)
& zero = multiplication(X1,X0) )
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| addition(X1,X0) != one
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( addition(X1,X0) = one
& zero = multiplication(X0,X1)
& zero = multiplication(X1,X0) )
<=> complement(X0,X1) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X4,X3] :
( ( zero = multiplication(X4,X3)
& one = addition(X3,X4)
& zero = multiplication(X3,X4) )
<=> complement(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f137,plain,
sF8 = addition(sK1,sF6),
inference(backward_demodulation,[],[f135,f136]) ).
fof(f136,plain,
sK1 = sF5,
inference(forward_demodulation,[],[f132,f75]) ).
fof(f75,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f132,plain,
multiplication(one,sK1) = sF5,
inference(backward_demodulation,[],[f89,f131]) ).
fof(f131,plain,
one = sF4,
inference(backward_demodulation,[],[f88,f128]) ).
fof(f128,plain,
one = addition(sK0,sF3),
inference(superposition,[],[f121,f76]) ).
fof(f121,plain,
one = addition(sF3,sK0),
inference(resolution,[],[f69,f98]) ).
fof(f98,plain,
complement(sK0,sF3),
inference(subsumption_resolution,[],[f96,f64]) ).
fof(f64,plain,
test(sK0),
inference(cnf_transformation,[],[f47]) ).
fof(f96,plain,
( complement(sK0,sF3)
| ~ test(sK0) ),
inference(superposition,[],[f86,f87]) ).
fof(f87,plain,
c(sK0) = sF3,
introduced(function_definition,[]) ).
fof(f88,plain,
addition(sK0,sF3) = sF4,
introduced(function_definition,[]) ).
fof(f89,plain,
sF5 = multiplication(sF4,sK1),
introduced(function_definition,[]) ).
fof(f135,plain,
addition(sF5,sF6) = sF8,
inference(backward_demodulation,[],[f92,f134]) ).
fof(f134,plain,
sF7 = sF6,
inference(forward_demodulation,[],[f133,f75]) ).
fof(f133,plain,
sF7 = multiplication(one,sF6),
inference(backward_demodulation,[],[f91,f131]) ).
fof(f91,plain,
sF7 = multiplication(sF4,sF6),
introduced(function_definition,[]) ).
fof(f92,plain,
sF8 = addition(sF5,sF7),
introduced(function_definition,[]) ).
fof(f168,plain,
( ~ leq(sF8,one)
| ~ leq(one,one) ),
inference(backward_demodulation,[],[f93,f165]) ).
fof(f93,plain,
( ~ leq(sF8,one)
| ~ leq(one,sF8) ),
inference(definition_folding,[],[f63,f92,f91,f90,f88,f87,f89,f88,f87,f92,f91,f90,f88,f87,f89,f88,f87]) ).
fof(f63,plain,
( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
| ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) ),
inference(cnf_transformation,[],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 00:36:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.54 % (3540)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.55 % (3548)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.55 % (3555)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.55 % (3539)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55 % (3548)First to succeed.
% 0.19/0.56 % (3547)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.56 TRYING [1]
% 0.19/0.56 % (3540)Instruction limit reached!
% 0.19/0.56 % (3540)------------------------------
% 0.19/0.56 % (3540)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56 TRYING [2]
% 0.19/0.56 TRYING [3]
% 0.19/0.56 % (3556)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.57 % (3548)Refutation found. Thanks to Tanya!
% 0.19/0.57 % SZS status Theorem for theBenchmark
% 0.19/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.57 % (3548)------------------------------
% 0.19/0.57 % (3548)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57 % (3548)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57 % (3548)Termination reason: Refutation
% 0.19/0.57
% 0.19/0.57 % (3548)Memory used [KB]: 1023
% 0.19/0.57 % (3548)Time elapsed: 0.131 s
% 0.19/0.57 % (3548)Instructions burned: 7 (million)
% 0.19/0.57 % (3548)------------------------------
% 0.19/0.57 % (3548)------------------------------
% 0.19/0.57 % (3532)Success in time 0.219 s
%------------------------------------------------------------------------------