TSTP Solution File: KLE026+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE026+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 : Tue Apr 30 13:11:42 EDT 2024
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 29 unt; 0 def)
% Number of atoms : 119 ( 55 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 93 ( 28 ~; 20 |; 31 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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 : 94 ( 80 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4438,plain,
$false,
inference(subsumption_resolution,[],[f4426,f43]) ).
fof(f43,plain,
~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( ~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2))
& multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2)
& test(sK2)
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f31]) ).
fof(f31,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(sK1,sK0),multiplication(sK0,sK2))
& multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2)
& test(sK2)
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f27,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,[],[f26]) ).
fof(f26,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,[],[f19]) ).
fof(f19,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,[],[f18]) ).
fof(f18,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,[],[f17]) ).
fof(f17,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(f4426,plain,
leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
inference(superposition,[],[f4332,f168]) ).
fof(f168,plain,
multiplication(sK1,sK0) = multiplication(sK1,multiplication(sK0,sK2)),
inference(superposition,[],[f62,f42]) ).
fof(f42,plain,
multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f62,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
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(f4332,plain,
! [X0] : leq(multiplication(sK1,X0),X0),
inference(superposition,[],[f1377,f4160]) ).
fof(f4160,plain,
! [X0] : addition(X0,multiplication(sK1,X0)) = X0,
inference(forward_demodulation,[],[f4044,f48]) ).
fof(f48,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f4044,plain,
! [X0] : multiplication(one,X0) = addition(X0,multiplication(sK1,X0)),
inference(superposition,[],[f492,f1279]) ).
fof(f1279,plain,
one = addition(one,sK1),
inference(superposition,[],[f1259,f53]) ).
fof(f53,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f1259,plain,
one = addition(sK1,one),
inference(superposition,[],[f106,f128]) ).
fof(f128,plain,
one = addition(sK1,sK3(sK1)),
inference(resolution,[],[f80,f40]) ).
fof(f40,plain,
test(sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f80,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK3(X0)) ),
inference(resolution,[],[f58,f51]) ).
fof(f51,plain,
! [X0] :
( complement(sK3(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK3(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f34,f35]) ).
fof(f35,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
fof(f58,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,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,[],[f38]) ).
fof(f38,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(f23,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
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(f106,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f61,f49]) ).
fof(f49,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f61,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
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(f492,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f64,f48]) ).
fof(f64,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
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(f1377,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f1272,f53]) ).
fof(f1272,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f1268]) ).
fof(f1268,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f60,f106]) ).
fof(f60,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE026+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:04:14 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (26369)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (26372)WARNING: value z3 for option sas not known
% 0.14/0.37 % (26372)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (26373)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (26371)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (26375)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (26376)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (26374)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (26370)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [4]
% 0.14/0.40 TRYING [3]
% 0.14/0.41 TRYING [5]
% 0.21/0.44 TRYING [4]
% 0.21/0.47 % (26372)First to succeed.
% 0.21/0.47 % (26372)Refutation found. Thanks to Tanya!
% 0.21/0.47 % SZS status Theorem for theBenchmark
% 0.21/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.47 % (26372)------------------------------
% 0.21/0.47 % (26372)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.47 % (26372)Termination reason: Refutation
% 0.21/0.47
% 0.21/0.47 % (26372)Memory used [KB]: 2389
% 0.21/0.47 % (26372)Time elapsed: 0.101 s
% 0.21/0.47 % (26372)Instructions burned: 212 (million)
% 0.21/0.47 % (26372)------------------------------
% 0.21/0.47 % (26372)------------------------------
% 0.21/0.47 % (26369)Success in time 0.117 s
%------------------------------------------------------------------------------