TSTP Solution File: KLE021+4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE021+4 : 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 : 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 : Tue Apr 30 13:11:41 EDT 2024
% Result : Theorem 0.16s 0.39s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 107 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 109 ( 46 ~; 32 |; 18 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 57 ( 53 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f128,plain,
$false,
inference(resolution,[],[f127,f98]) ).
fof(f98,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f93]) ).
fof(f93,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f67,f54]) ).
fof(f54,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(f67,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,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) ).
fof(f127,plain,
~ leq(sK0,sK0),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f126,plain,
( ~ leq(sK0,sK0)
| ~ leq(sK0,sK0) ),
inference(forward_demodulation,[],[f125,f53]) ).
fof(f53,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(f125,plain,
( ~ leq(multiplication(one,sK0),sK0)
| ~ leq(sK0,sK0) ),
inference(forward_demodulation,[],[f124,f120]) ).
fof(f120,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f91,f47]) ).
fof(f47,plain,
test(sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
( ( ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0)
| ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))) )
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f30,f38]) ).
fof(f38,plain,
( ? [X0,X1] :
( ( ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
| ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) )
& test(X1) )
=> ( ( ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0)
| ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))) )
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0,X1] :
( ( ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
| ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) )
& test(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( test(X4)
=> ( leq(addition(multiplication(X4,X3),multiplication(c(X4),X3)),X3)
& leq(X3,addition(multiplication(X4,X3),multiplication(c(X4),X3))) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4] :
( test(X4)
=> ( leq(addition(multiplication(X4,X3),multiplication(c(X4),X3)),X3)
& leq(X3,addition(multiplication(X4,X3),multiplication(c(X4),X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f91,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f90,f58]) ).
fof(f58,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(f90,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f65,f72]) ).
fof(f72,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X4] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f65,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,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,[],[f45]) ).
fof(f45,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,[],[f27]) ).
fof(f27,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(f124,plain,
( ~ leq(sK0,sK0)
| ~ leq(multiplication(addition(sK1,c(sK1)),sK0),sK0) ),
inference(forward_demodulation,[],[f123,f53]) ).
fof(f123,plain,
( ~ leq(sK0,multiplication(one,sK0))
| ~ leq(multiplication(addition(sK1,c(sK1)),sK0),sK0) ),
inference(backward_demodulation,[],[f74,f120]) ).
fof(f74,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),sK0),sK0)
| ~ leq(sK0,multiplication(addition(sK1,c(sK1)),sK0)) ),
inference(forward_demodulation,[],[f73,f71]) ).
fof(f71,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(f73,plain,
( ~ leq(sK0,multiplication(addition(sK1,c(sK1)),sK0))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0) ),
inference(backward_demodulation,[],[f48,f71]) ).
fof(f48,plain,
( ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0)
| ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))) ),
inference(cnf_transformation,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE021+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n027.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Apr 30 05:28:32 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (10643)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (10647)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38 % (10646)WARNING: value z3 for option sas not known
% 0.16/0.38 % (10644)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38 % (10648)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)
% 0.16/0.38 % (10649)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)
% 0.16/0.38 % (10645)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38 % (10650)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)
% 0.16/0.38 % (10646)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)
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 % (10649)First to succeed.
% 0.16/0.39 % (10649)Refutation found. Thanks to Tanya!
% 0.16/0.39 % SZS status Theorem for theBenchmark
% 0.16/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.39 % (10649)------------------------------
% 0.16/0.39 % (10649)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.39 % (10649)Termination reason: Refutation
% 0.16/0.39
% 0.16/0.39 % (10649)Memory used [KB]: 897
% 0.16/0.39 % (10649)Time elapsed: 0.007 s
% 0.16/0.39 % (10649)Instructions burned: 8 (million)
% 0.16/0.39 % (10649)------------------------------
% 0.16/0.39 % (10649)------------------------------
% 0.16/0.39 % (10643)Success in time 0.023 s
%------------------------------------------------------------------------------