TSTP Solution File: GRP002-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP002-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Mon May 20 21:13:50 EDT 2024
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4367,plain,
$false,
inference(subsumption_resolution,[],[f4356,f12]) ).
fof(f12,axiom,
identity != multiply(k,inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
fof(f4356,plain,
identity = multiply(k,inverse(b)),
inference(superposition,[],[f5,f4345]) ).
fof(f4345,plain,
inverse(b) = inverse(k),
inference(forward_demodulation,[],[f4344,f241]) ).
fof(f241,plain,
! [X0] : inverse(X0) = multiply(X0,X0),
inference(forward_demodulation,[],[f196,f4]) ).
fof(f4,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f196,plain,
! [X0] : multiply(X0,X0) = multiply(inverse(X0),identity),
inference(superposition,[],[f41,f6]) ).
fof(f6,axiom,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
fof(f41,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f24,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f24,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f3,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f4344,plain,
multiply(b,b) = inverse(k),
inference(forward_demodulation,[],[f4334,f2766]) ).
fof(f2766,plain,
inverse(k) = multiply(inverse(h),multiply(b,d)),
inference(superposition,[],[f41,f2651]) ).
fof(f2651,plain,
multiply(h,inverse(k)) = multiply(b,d),
inference(forward_demodulation,[],[f2631,f1136]) ).
fof(f1136,plain,
inverse(k) = multiply(h,inverse(d)),
inference(forward_demodulation,[],[f1135,f241]) ).
fof(f1135,plain,
multiply(h,inverse(d)) = multiply(k,k),
inference(forward_demodulation,[],[f1126,f4]) ).
fof(f1126,plain,
multiply(h,inverse(d)) = multiply(k,multiply(k,identity)),
inference(superposition,[],[f45,f552]) ).
fof(f552,plain,
identity = multiply(k,multiply(h,inverse(d))),
inference(superposition,[],[f36,f143]) ).
fof(f143,plain,
d = multiply(k,h),
inference(forward_demodulation,[],[f138,f4]) ).
fof(f138,plain,
multiply(d,identity) = multiply(k,h),
inference(superposition,[],[f137,f2]) ).
fof(f137,plain,
! [X0] : multiply(k,X0) = multiply(d,multiply(inverse(h),X0)),
inference(forward_demodulation,[],[f31,f110]) ).
fof(f110,plain,
d = j,
inference(superposition,[],[f104,f10]) ).
fof(f10,axiom,
multiply(h,b) = j,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
fof(f104,plain,
d = multiply(h,b),
inference(forward_demodulation,[],[f99,f4]) ).
fof(f99,plain,
multiply(h,b) = multiply(d,identity),
inference(superposition,[],[f30,f2]) ).
fof(f30,plain,
! [X0] : multiply(d,multiply(inverse(b),X0)) = multiply(h,X0),
inference(superposition,[],[f3,f9]) ).
fof(f9,axiom,
multiply(d,inverse(b)) = h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
fof(f31,plain,
! [X0] : multiply(j,multiply(inverse(h),X0)) = multiply(k,X0),
inference(superposition,[],[f3,f11]) ).
fof(f11,axiom,
multiply(j,inverse(h)) = k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
fof(f36,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f3,f5]) ).
fof(f45,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,X1))) = X1,
inference(forward_demodulation,[],[f44,f1]) ).
fof(f44,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(X0,multiply(X0,X1))),
inference(forward_demodulation,[],[f27,f3]) ).
fof(f27,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(multiply(X0,X0),X1)),
inference(superposition,[],[f3,f6]) ).
fof(f2631,plain,
multiply(b,d) = multiply(h,multiply(h,inverse(d))),
inference(superposition,[],[f45,f2612]) ).
fof(f2612,plain,
inverse(d) = multiply(h,multiply(b,d)),
inference(superposition,[],[f46,f2224]) ).
fof(f2224,plain,
multiply(inverse(h),inverse(d)) = multiply(b,d),
inference(superposition,[],[f242,f241]) ).
fof(f242,plain,
! [X0] : multiply(b,X0) = multiply(inverse(h),multiply(d,X0)),
inference(forward_demodulation,[],[f204,f110]) ).
fof(f204,plain,
! [X0] : multiply(b,X0) = multiply(inverse(h),multiply(j,X0)),
inference(superposition,[],[f41,f33]) ).
fof(f33,plain,
! [X0] : multiply(h,multiply(b,X0)) = multiply(j,X0),
inference(superposition,[],[f3,f10]) ).
fof(f46,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f28,f1]) ).
fof(f28,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f3,f5]) ).
fof(f4334,plain,
multiply(b,b) = multiply(inverse(h),multiply(b,d)),
inference(superposition,[],[f242,f4322]) ).
fof(f4322,plain,
multiply(d,b) = multiply(b,d),
inference(forward_demodulation,[],[f4309,f366]) ).
fof(f366,plain,
! [X0] : multiply(b,X0) = multiply(a,multiply(a,multiply(c,X0))),
inference(superposition,[],[f45,f32]) ).
fof(f32,plain,
! [X0] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[],[f3,f7]) ).
fof(f7,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f4309,plain,
multiply(d,b) = multiply(a,multiply(a,multiply(c,d))),
inference(superposition,[],[f45,f4300]) ).
fof(f4300,plain,
multiply(c,d) = multiply(a,multiply(d,b)),
inference(forward_demodulation,[],[f4281,f2317]) ).
fof(f2317,plain,
multiply(c,d) = multiply(b,multiply(b,a)),
inference(superposition,[],[f45,f2196]) ).
fof(f2196,plain,
a = multiply(b,multiply(c,d)),
inference(forward_demodulation,[],[f2161,f302]) ).
fof(f302,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = X0,
inference(forward_demodulation,[],[f276,f4]) ).
fof(f276,plain,
! [X0] : multiply(X0,identity) = multiply(inverse(X0),inverse(X0)),
inference(superposition,[],[f46,f6]) ).
fof(f2161,plain,
multiply(inverse(a),inverse(a)) = multiply(b,multiply(c,d)),
inference(superposition,[],[f197,f387]) ).
fof(f387,plain,
inverse(a) = multiply(c,multiply(c,d)),
inference(superposition,[],[f45,f8]) ).
fof(f8,axiom,
multiply(c,inverse(a)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
fof(f197,plain,
! [X0] : multiply(b,X0) = multiply(inverse(a),multiply(c,X0)),
inference(superposition,[],[f41,f32]) ).
fof(f4281,plain,
multiply(b,multiply(b,a)) = multiply(a,multiply(d,b)),
inference(superposition,[],[f45,f4255]) ).
fof(f4255,plain,
a = multiply(b,multiply(a,multiply(d,b))),
inference(forward_demodulation,[],[f4254,f4]) ).
fof(f4254,plain,
multiply(a,identity) = multiply(b,multiply(a,multiply(d,b))),
inference(forward_demodulation,[],[f4213,f475]) ).
fof(f475,plain,
multiply(d,b) = multiply(c,multiply(a,c)),
inference(superposition,[],[f84,f399]) ).
fof(f399,plain,
b = multiply(a,multiply(a,c)),
inference(superposition,[],[f45,f7]) ).
fof(f84,plain,
! [X0] : multiply(c,X0) = multiply(d,multiply(a,X0)),
inference(superposition,[],[f3,f78]) ).
fof(f78,plain,
c = multiply(d,a),
inference(forward_demodulation,[],[f73,f4]) ).
fof(f73,plain,
multiply(c,identity) = multiply(d,a),
inference(superposition,[],[f29,f2]) ).
fof(f29,plain,
! [X0] : multiply(c,multiply(inverse(a),X0)) = multiply(d,X0),
inference(superposition,[],[f3,f8]) ).
fof(f4213,plain,
multiply(a,identity) = multiply(b,multiply(a,multiply(c,multiply(a,c)))),
inference(superposition,[],[f366,f47]) ).
fof(f47,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))),
inference(forward_demodulation,[],[f35,f3]) ).
fof(f35,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,multiply(multiply(X0,X1),multiply(X0,X1)))),
inference(superposition,[],[f3,f6]) ).
fof(f5,axiom,
! [X0] : identity = multiply(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP002-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n006.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 : Sun May 19 04:18:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.36 % (30917)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (30920)WARNING: value z3 for option sas not known
% 0.20/0.37 % (30918)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (30921)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (30919)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (30920)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)
% 0.20/0.37 % (30922)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)
% 0.20/0.37 % (30923)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)
% 0.20/0.37 % (30924)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)
% 0.20/0.37 TRYING [1]
% 0.20/0.37 TRYING [2]
% 0.20/0.38 TRYING [3]
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 TRYING [4]
% 0.20/0.38 TRYING [3]
% 0.20/0.39 TRYING [5]
% 0.20/0.39 TRYING [4]
% 0.20/0.41 TRYING [6]
% 0.20/0.43 TRYING [5]
% 0.20/0.46 % (30920)First to succeed.
% 0.20/0.46 % (30920)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30917"
% 0.20/0.47 % (30920)Refutation found. Thanks to Tanya!
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47 % (30920)------------------------------
% 0.20/0.47 % (30920)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.47 % (30920)Termination reason: Refutation
% 0.20/0.47
% 0.20/0.47 % (30920)Memory used [KB]: 2380
% 0.20/0.47 % (30920)Time elapsed: 0.092 s
% 0.20/0.47 % (30920)Instructions burned: 189 (million)
% 0.20/0.47 % (30917)Success in time 0.108 s
%------------------------------------------------------------------------------