TSTP Solution File: KLE027+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE027+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 13:11:43 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 27 unt; 0 def)
% Number of atoms : 126 ( 63 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 107 ( 38 ~; 28 |; 27 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 100 ( 80 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f411,plain,
$false,
inference(trivial_inequality_removal,[],[f410]) ).
fof(f410,plain,
addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)) != addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),
inference(backward_demodulation,[],[f298,f408]) ).
fof(f408,plain,
! [X0] : multiplication(sK3,X0) = multiplication(sK3,multiplication(sK3,X0)),
inference(superposition,[],[f58,f395]) ).
fof(f395,plain,
sK3 = multiplication(sK3,sK3),
inference(forward_demodulation,[],[f386,f44]) ).
fof(f44,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f386,plain,
multiplication(sK3,one) = multiplication(sK3,sK3),
inference(superposition,[],[f294,f115]) ).
fof(f115,plain,
one = addition(sK3,sK5(sK3)),
inference(resolution,[],[f74,f38]) ).
fof(f38,plain,
test(sK3),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)) != addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))
& test(sK4)
& test(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f26,f29]) ).
fof(f29,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(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)) != addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))
& test(sK4)
& test(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f26,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,[],[f25]) ).
fof(f25,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,[],[f19]) ).
fof(f19,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,[],[f18]) ).
fof(f18,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,[],[f17]) ).
fof(f17,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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f74,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK5(X0)) ),
inference(resolution,[],[f55,f48]) ).
fof(f48,plain,
! [X0] :
( complement(sK5(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK5(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f32,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f31]) ).
fof(f31,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(f55,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,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,[],[f36]) ).
fof(f36,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(f294,plain,
! [X0] : multiplication(sK3,X0) = multiplication(sK3,addition(X0,sK5(sK3))),
inference(forward_demodulation,[],[f245,f43]) ).
fof(f43,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f245,plain,
! [X0] : multiplication(sK3,addition(X0,sK5(sK3))) = addition(multiplication(sK3,X0),zero),
inference(superposition,[],[f59,f77]) ).
fof(f77,plain,
zero = multiplication(sK3,sK5(sK3)),
inference(resolution,[],[f70,f38]) ).
fof(f70,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK5(X0)) ),
inference(resolution,[],[f53,f48]) ).
fof(f53,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f58,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(f298,plain,
addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)) != addition(multiplication(sK3,multiplication(sK3,sK0)),multiplication(c(sK3),sK2)),
inference(backward_demodulation,[],[f40,f297]) ).
fof(f297,plain,
! [X0,X1] : multiplication(sK3,X1) = multiplication(sK3,addition(X1,multiplication(c(sK3),X0))),
inference(forward_demodulation,[],[f248,f43]) ).
fof(f248,plain,
! [X0,X1] : addition(multiplication(sK3,X1),zero) = multiplication(sK3,addition(X1,multiplication(c(sK3),X0))),
inference(superposition,[],[f59,f154]) ).
fof(f154,plain,
! [X0] : zero = multiplication(sK3,multiplication(c(sK3),X0)),
inference(forward_demodulation,[],[f138,f42]) ).
fof(f42,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f138,plain,
! [X0] : multiplication(zero,X0) = multiplication(sK3,multiplication(c(sK3),X0)),
inference(superposition,[],[f58,f111]) ).
fof(f111,plain,
zero = multiplication(sK3,c(sK3)),
inference(resolution,[],[f73,f38]) ).
fof(f73,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,c(X0)) ),
inference(resolution,[],[f54,f61]) ).
fof(f61,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,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(f54,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f40,plain,
addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)) != addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE027+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % 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 05:02:29 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (22372)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (22375)WARNING: value z3 for option sas not known
% 0.14/0.38 % (22374)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (22376)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (22373)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (22377)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)
% 0.14/0.38 % (22375)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)
% 0.14/0.38 % (22378)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)
% 0.14/0.38 % (22379)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 % (22378)First to succeed.
% 0.14/0.39 TRYING [4]
% 0.14/0.39 % (22378)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (22378)------------------------------
% 0.14/0.39 % (22378)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39 % (22378)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (22378)Memory used [KB]: 1036
% 0.14/0.39 % (22378)Time elapsed: 0.016 s
% 0.14/0.39 % (22378)Instructions burned: 25 (million)
% 0.14/0.39 % (22378)------------------------------
% 0.14/0.39 % (22378)------------------------------
% 0.14/0.39 % (22372)Success in time 0.032 s
%------------------------------------------------------------------------------