TSTP Solution File: KLE081+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE081+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 : n002.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 13:11:53 EDT 2024
% Result : Theorem 5.00s 1.09s
% Output : Refutation 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 91 ( 85 unt; 0 def)
% Number of atoms : 106 ( 105 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 23 ( 8 ~; 0 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 135 ( 133 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33364,plain,
$false,
inference(trivial_inequality_removal,[],[f33305]) ).
fof(f33305,plain,
zero != zero,
inference(superposition,[],[f31,f33209]) ).
fof(f33209,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(forward_demodulation,[],[f33064,f34]) ).
fof(f34,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f33064,plain,
! [X0] : multiplication(antidomain(X0),X0) = multiplication(zero,multiplication(antidomain(X0),X0)),
inference(superposition,[],[f8117,f32720]) ).
fof(f32720,plain,
! [X0] : zero = domain(multiplication(antidomain(X0),X0)),
inference(forward_demodulation,[],[f32719,f32]) ).
fof(f32,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
zero = domain(zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f32719,plain,
! [X0] : domain(zero) = domain(multiplication(antidomain(X0),X0)),
inference(forward_demodulation,[],[f32622,f35]) ).
fof(f35,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f32622,plain,
! [X0] : domain(zero) = domain(addition(multiplication(antidomain(X0),X0),zero)),
inference(superposition,[],[f92,f32460]) ).
fof(f32460,plain,
! [X0] : zero = addition(multiplication(antidomain(X0),domain(X0)),zero),
inference(forward_demodulation,[],[f32459,f34]) ).
fof(f32459,plain,
! [X0] : multiplication(zero,multiplication(antidomain(X0),domain(X0))) = addition(multiplication(antidomain(X0),domain(X0)),multiplication(zero,multiplication(antidomain(X0),domain(X0)))),
inference(forward_demodulation,[],[f32458,f32]) ).
fof(f32458,plain,
! [X0] : multiplication(domain(zero),multiplication(antidomain(X0),domain(X0))) = addition(multiplication(antidomain(X0),domain(X0)),multiplication(domain(zero),multiplication(antidomain(X0),domain(X0)))),
inference(forward_demodulation,[],[f32281,f13287]) ).
fof(f13287,plain,
! [X0] : domain(X0) = domain(antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f13286,f90]) ).
fof(f90,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[],[f82,f37]) ).
fof(f37,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(f82,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(superposition,[],[f43,f37]) ).
fof(f43,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] : domain(multiplication(X3,X4)) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f13286,plain,
! [X0] : domain(domain(X0)) = domain(antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f13184,f9406]) ).
fof(f9406,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(domain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f9367,f37]) ).
fof(f9367,plain,
! [X0] : multiplication(one,antidomain(antidomain(X0))) = multiplication(domain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f772,f9332]) ).
fof(f9332,plain,
! [X0] : one = addition(domain(X0),domain(antidomain(X0))),
inference(forward_demodulation,[],[f9315,f52]) ).
fof(f52,plain,
! [X0] : one = addition(one,domain(X0)),
inference(superposition,[],[f41,f39]) ).
fof(f39,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] : one = addition(domain(X0),one),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(domain(X3),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f41,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/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f9315,plain,
! [X0] : addition(one,domain(antidomain(X0))) = addition(domain(X0),domain(antidomain(X0))),
inference(superposition,[],[f994,f8174]) ).
fof(f8174,plain,
! [X0] : domain(antidomain(X0)) = addition(domain(antidomain(X0)),antidomain(X0)),
inference(superposition,[],[f7076,f8117]) ).
fof(f7076,plain,
! [X0,X1] : addition(X1,multiplication(X1,antidomain(X0))) = X1,
inference(forward_demodulation,[],[f6985,f36]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f6985,plain,
! [X0,X1] : multiplication(X1,one) = addition(X1,multiplication(X1,antidomain(X0))),
inference(superposition,[],[f528,f1023]) ).
fof(f1023,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f993,f29]) ).
fof(f29,plain,
! [X1] : one = addition(domain(X1),antidomain(X1)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( zero != multiplication(antidomain(sK0),sK0)
& ! [X1] :
( zero = multiplication(domain(X1),antidomain(X1))
& one = addition(domain(X1),antidomain(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f27]) ).
fof(f27,plain,
( ? [X0] :
( zero != multiplication(antidomain(X0),X0)
& ! [X1] :
( zero = multiplication(domain(X1),antidomain(X1))
& one = addition(domain(X1),antidomain(X1)) ) )
=> ( zero != multiplication(antidomain(sK0),sK0)
& ! [X1] :
( zero = multiplication(domain(X1),antidomain(X1))
& one = addition(domain(X1),antidomain(X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
? [X0] :
( zero != multiplication(antidomain(X0),X0)
& ! [X1] :
( zero = multiplication(domain(X1),antidomain(X1))
& one = addition(domain(X1),antidomain(X1)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
~ ! [X0] :
( ! [X1] :
( zero = multiplication(domain(X1),antidomain(X1))
& one = addition(domain(X1),antidomain(X1)) )
=> zero = multiplication(antidomain(X0),X0) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X3] :
( ! [X4] :
( zero = multiplication(domain(X4),antidomain(X4))
& one = addition(domain(X4),antidomain(X4)) )
=> zero = multiplication(antidomain(X3),X3) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X3] :
( ! [X4] :
( zero = multiplication(domain(X4),antidomain(X4))
& one = addition(domain(X4),antidomain(X4)) )
=> zero = multiplication(antidomain(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f993,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = addition(one,antidomain(X0)),
inference(superposition,[],[f299,f38]) ).
fof(f38,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(f299,plain,
! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(antidomain(X0),X1)),
inference(superposition,[],[f44,f29]) ).
fof(f44,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f25,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/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f528,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f46,f36]) ).
fof(f46,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/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f994,plain,
! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(X1,antidomain(X0))),
inference(superposition,[],[f299,f41]) ).
fof(f772,plain,
! [X0,X1] : multiplication(X1,antidomain(X0)) = multiplication(addition(X1,domain(X0)),antidomain(X0)),
inference(forward_demodulation,[],[f733,f35]) ).
fof(f733,plain,
! [X0,X1] : multiplication(addition(X1,domain(X0)),antidomain(X0)) = addition(multiplication(X1,antidomain(X0)),zero),
inference(superposition,[],[f47,f30]) ).
fof(f30,plain,
! [X1] : zero = multiplication(domain(X1),antidomain(X1)),
inference(cnf_transformation,[],[f28]) ).
fof(f47,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/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f13184,plain,
! [X0] : domain(domain(X0)) = domain(multiplication(domain(X0),antidomain(antidomain(X0)))),
inference(superposition,[],[f9505,f568]) ).
fof(f568,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[],[f534,f51]) ).
fof(f51,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f41,f35]) ).
fof(f534,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = addition(zero,multiplication(domain(X0),X1)),
inference(superposition,[],[f46,f30]) ).
fof(f9505,plain,
! [X0,X1] : domain(X1) = domain(multiplication(X1,addition(X0,antidomain(X0)))),
inference(forward_demodulation,[],[f9438,f36]) ).
fof(f9438,plain,
! [X0,X1] : domain(multiplication(X1,one)) = domain(multiplication(X1,addition(X0,antidomain(X0)))),
inference(superposition,[],[f43,f9356]) ).
fof(f9356,plain,
! [X0] : one = domain(addition(X0,antidomain(X0))),
inference(superposition,[],[f9332,f42]) ).
fof(f42,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3,X4] : domain(addition(X3,X4)) = addition(domain(X3),domain(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
fof(f32281,plain,
! [X0] : multiplication(domain(zero),multiplication(antidomain(X0),domain(antidomain(antidomain(X0))))) = addition(multiplication(antidomain(X0),domain(antidomain(antidomain(X0)))),multiplication(domain(zero),multiplication(antidomain(X0),domain(antidomain(antidomain(X0)))))),
inference(superposition,[],[f229,f9161]) ).
fof(f9161,plain,
! [X0] : zero = multiplication(antidomain(X0),antidomain(antidomain(X0))),
inference(superposition,[],[f7262,f8117]) ).
fof(f7262,plain,
! [X0,X1] : zero = multiplication(multiplication(domain(X0),antidomain(X1)),antidomain(X0)),
inference(forward_demodulation,[],[f7215,f30]) ).
fof(f7215,plain,
! [X0,X1] : multiplication(domain(X0),antidomain(X0)) = multiplication(multiplication(domain(X0),antidomain(X1)),antidomain(X0)),
inference(superposition,[],[f757,f7076]) ).
fof(f757,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(forward_demodulation,[],[f721,f51]) ).
fof(f721,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = addition(zero,multiplication(X1,antidomain(X0))),
inference(superposition,[],[f47,f30]) ).
fof(f229,plain,
! [X0,X1] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(superposition,[],[f40,f43]) ).
fof(f40,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : multiplication(domain(X3),X3) = addition(X3,multiplication(domain(X3),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f92,plain,
! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = domain(addition(multiplication(X0,X1),X2)),
inference(forward_demodulation,[],[f87,f42]) ).
fof(f87,plain,
! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = addition(domain(multiplication(X0,X1)),domain(X2)),
inference(superposition,[],[f42,f43]) ).
fof(f8117,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(forward_demodulation,[],[f8116,f37]) ).
fof(f8116,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[],[f8006,f52]) ).
fof(f8006,plain,
! [X0] : multiplication(domain(X0),X0) = multiplication(addition(one,domain(X0)),X0),
inference(superposition,[],[f718,f40]) ).
fof(f718,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f47,f37]) ).
fof(f31,plain,
zero != multiplication(antidomain(sK0),sK0),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE081+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 05:23:10 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % (14007)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (14009)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (14010)WARNING: value z3 for option sas not known
% 0.22/0.38 % (14011)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (14012)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)
% 0.22/0.38 % (14013)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)
% 0.22/0.38 % (14014)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)
% 0.22/0.38 % (14010)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)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 % (14008)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.40 TRYING [4]
% 0.22/0.41 TRYING [3]
% 0.22/0.43 TRYING [5]
% 0.22/0.44 TRYING [4]
% 0.22/0.48 TRYING [6]
% 1.30/0.55 TRYING [5]
% 2.22/0.69 TRYING [7]
% 3.28/0.85 TRYING [6]
% 5.00/1.09 % (14010)First to succeed.
% 5.00/1.09 % (14010)Refutation found. Thanks to Tanya!
% 5.00/1.09 % SZS status Theorem for theBenchmark
% 5.00/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 5.00/1.09 % (14010)------------------------------
% 5.00/1.09 % (14010)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.00/1.09 % (14010)Termination reason: Refutation
% 5.00/1.09
% 5.00/1.09 % (14010)Memory used [KB]: 10159
% 5.00/1.09 % (14010)Time elapsed: 0.694 s
% 5.00/1.09 % (14010)Instructions burned: 1730 (million)
% 5.00/1.09 % (14010)------------------------------
% 5.00/1.09 % (14010)------------------------------
% 5.00/1.09 % (14007)Success in time 0.72 s
%------------------------------------------------------------------------------