TSTP Solution File: ANA133-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 18:41:54 EDT 2024
% Result : Unsatisfiable 26.53s 4.15s
% Output : Refutation 26.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 65 unt; 0 def)
% Number of atoms : 65 ( 64 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f260142,plain,
$false,
inference(subsumption_resolution,[],[f260141,f17]) ).
fof(f17,axiom,
! [X3] : d(X3) != times(x,cos(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f260141,plain,
times(x,cos(x)) = d('+'(cos(x),times(x,sin(x)))),
inference(forward_demodulation,[],[f260140,f54]) ).
fof(f54,plain,
cos(x) = d(sin(x)),
inference(forward_demodulation,[],[f47,f30]) ).
fof(f30,plain,
! [X0] : times(X0,one) = X0,
inference(superposition,[],[f3,f7]) ).
fof(f7,axiom,
! [X0] : times(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_one) ).
fof(f3,axiom,
! [X0,X1] : times(X0,X1) = times(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_times) ).
fof(f47,plain,
d(sin(x)) = times(cos(x),one),
inference(superposition,[],[f15,f12]) ).
fof(f12,axiom,
one = d(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_x) ).
fof(f15,axiom,
! [X3] : d(sin(X3)) = times(cos(X3),d(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_sin) ).
fof(f260140,plain,
times(x,d(sin(x))) = d('+'(cos(x),times(x,sin(x)))),
inference(forward_demodulation,[],[f260139,f691]) ).
fof(f691,plain,
! [X0] : minus(minus(X0)) = X0,
inference(forward_demodulation,[],[f681,f21]) ).
fof(f21,plain,
! [X0] : '+'(X0,zero) = X0,
inference(superposition,[],[f1,f5]) ).
fof(f5,axiom,
! [X0] : '+'(zero,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
fof(f1,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).
fof(f681,plain,
! [X0] : '+'(X0,zero) = minus(minus(X0)),
inference(superposition,[],[f441,f9]) ).
fof(f9,axiom,
! [X0] : zero = '+'(X0,minus(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus) ).
fof(f441,plain,
! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = X1,
inference(forward_demodulation,[],[f423,f5]) ).
fof(f423,plain,
! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = '+'(zero,X1),
inference(superposition,[],[f2,f9]) ).
fof(f2,axiom,
! [X2,X0,X1] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associtivity_of_plus) ).
fof(f260139,plain,
times(x,d(sin(x))) = d('+'(cos(x),times(x,minus(minus(sin(x)))))),
inference(forward_demodulation,[],[f260138,f1]) ).
fof(f260138,plain,
times(x,d(sin(x))) = d('+'(times(x,minus(minus(sin(x)))),cos(x))),
inference(forward_demodulation,[],[f260137,f691]) ).
fof(f260137,plain,
d('+'(times(x,minus(minus(sin(x)))),cos(x))) = times(x,minus(minus(d(sin(x))))),
inference(forward_demodulation,[],[f259996,f38135]) ).
fof(f38135,plain,
! [X0] : minus(d(X0)) = d(minus(X0)),
inference(forward_demodulation,[],[f38134,f37972]) ).
fof(f37972,plain,
! [X0] : minus(X0) = times(X0,minus(one)),
inference(forward_demodulation,[],[f37971,f5]) ).
fof(f37971,plain,
! [X0] : '+'(zero,minus(X0)) = times(X0,minus(one)),
inference(forward_demodulation,[],[f37910,f1]) ).
fof(f37910,plain,
! [X0] : '+'(minus(X0),zero) = times(X0,minus(one)),
inference(superposition,[],[f697,f29868]) ).
fof(f29868,plain,
! [X0] : zero = '+'(X0,times(X0,minus(one))),
inference(forward_demodulation,[],[f29867,f29]) ).
fof(f29,plain,
! [X0] : zero = times(X0,zero),
inference(superposition,[],[f3,f6]) ).
fof(f6,axiom,
! [X0] : zero = times(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_zero) ).
fof(f29867,plain,
! [X0] : times(X0,zero) = '+'(X0,times(X0,minus(one))),
inference(forward_demodulation,[],[f29750,f3109]) ).
fof(f3109,plain,
minus(one) = d(minus(x)),
inference(forward_demodulation,[],[f3103,f21]) ).
fof(f3103,plain,
'+'(minus(one),zero) = d(minus(x)),
inference(superposition,[],[f697,f2209]) ).
fof(f2209,plain,
zero = '+'(one,d(minus(x))),
inference(forward_demodulation,[],[f2186,f10]) ).
fof(f10,axiom,
zero = d(zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_zero) ).
fof(f2186,plain,
d(zero) = '+'(one,d(minus(x))),
inference(superposition,[],[f57,f9]) ).
fof(f57,plain,
! [X0] : d('+'(x,X0)) = '+'(one,d(X0)),
inference(superposition,[],[f13,f12]) ).
fof(f13,axiom,
! [X3,X4] : d('+'(X3,X4)) = '+'(d(X3),d(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_plus) ).
fof(f29750,plain,
! [X0] : times(X0,zero) = '+'(X0,times(X0,d(minus(x)))),
inference(superposition,[],[f723,f2209]) ).
fof(f723,plain,
! [X0,X1] : times(X0,'+'(one,X1)) = '+'(X0,times(X0,X1)),
inference(superposition,[],[f8,f30]) ).
fof(f8,axiom,
! [X2,X0,X1] : times(X0,'+'(X1,X2)) = '+'(times(X0,X1),times(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
fof(f697,plain,
! [X0,X1] : '+'(minus(X0),'+'(X0,X1)) = X1,
inference(superposition,[],[f441,f691]) ).
fof(f38134,plain,
! [X0] : d(times(X0,minus(one))) = minus(d(X0)),
inference(forward_demodulation,[],[f38133,f5]) ).
fof(f38133,plain,
! [X0] : d(times(X0,minus(one))) = '+'(zero,minus(d(X0))),
inference(forward_demodulation,[],[f38132,f29]) ).
fof(f38132,plain,
! [X0] : d(times(X0,minus(one))) = '+'(times(X0,zero),minus(d(X0))),
inference(forward_demodulation,[],[f38102,f113]) ).
fof(f113,plain,
zero = d(minus(one)),
inference(forward_demodulation,[],[f105,f10]) ).
fof(f105,plain,
d(zero) = d(minus(one)),
inference(superposition,[],[f66,f9]) ).
fof(f66,plain,
! [X0] : d(X0) = d('+'(one,X0)),
inference(forward_demodulation,[],[f56,f5]) ).
fof(f56,plain,
! [X0] : '+'(zero,d(X0)) = d('+'(one,X0)),
inference(superposition,[],[f13,f11]) ).
fof(f11,axiom,
zero = d(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_one) ).
fof(f38102,plain,
! [X0] : d(times(X0,minus(one))) = '+'(times(X0,d(minus(one))),minus(d(X0))),
inference(superposition,[],[f1093,f37972]) ).
fof(f1093,plain,
! [X0,X1] : d(times(X1,X0)) = '+'(times(X1,d(X0)),times(d(X1),X0)),
inference(superposition,[],[f14,f3]) ).
fof(f14,axiom,
! [X3,X4] : d(times(X3,X4)) = '+'(times(X3,d(X4)),times(X4,d(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_times) ).
fof(f259996,plain,
d('+'(times(x,minus(minus(sin(x)))),cos(x))) = times(x,minus(d(minus(sin(x))))),
inference(superposition,[],[f228751,f2609]) ).
fof(f2609,plain,
! [X0] : d('+'(X0,cos(x))) = '+'(minus(sin(x)),d(X0)),
inference(superposition,[],[f61,f292]) ).
fof(f292,plain,
d(cos(x)) = minus(sin(x)),
inference(forward_demodulation,[],[f270,f7]) ).
fof(f270,plain,
d(cos(x)) = minus(times(one,sin(x))),
inference(superposition,[],[f142,f12]) ).
fof(f142,plain,
! [X3] : d(cos(X3)) = minus(times(d(X3),sin(X3))),
inference(forward_demodulation,[],[f16,f3]) ).
fof(f16,axiom,
! [X3] : d(cos(X3)) = minus(times(sin(X3),d(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_cos) ).
fof(f61,plain,
! [X0,X1] : d('+'(X0,X1)) = '+'(d(X1),d(X0)),
inference(superposition,[],[f13,f1]) ).
fof(f228751,plain,
! [X0] : '+'(X0,d(times(x,minus(X0)))) = times(x,minus(d(X0))),
inference(forward_demodulation,[],[f5638,f38135]) ).
fof(f5638,plain,
! [X0] : times(x,d(minus(X0))) = '+'(X0,d(times(x,minus(X0)))),
inference(forward_demodulation,[],[f5067,f3]) ).
fof(f5067,plain,
! [X0] : times(x,d(minus(X0))) = '+'(X0,d(times(minus(X0),x))),
inference(superposition,[],[f441,f1119]) ).
fof(f1119,plain,
! [X0] : d(times(X0,x)) = '+'(X0,times(x,d(X0))),
inference(forward_demodulation,[],[f977,f30]) ).
fof(f977,plain,
! [X0] : d(times(X0,x)) = '+'(times(X0,one),times(x,d(X0))),
inference(superposition,[],[f14,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37 % Computer : n005.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 07:43:08 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.38 % (8932)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (8935)WARNING: value z3 for option sas not known
% 0.16/0.39 % (8933)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 % (8936)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39 % (8934)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39 % (8935)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)
% 0.16/0.39 % (8937)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)
% 0.16/0.39 % (8938)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)
% 0.16/0.39 % (8939)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)
% 0.16/0.40 TRYING [1]
% 0.16/0.40 TRYING [2]
% 0.16/0.40 TRYING [3]
% 0.16/0.40 TRYING [1]
% 0.16/0.40 TRYING [2]
% 0.16/0.41 TRYING [4]
% 0.23/0.41 TRYING [3]
% 0.23/0.45 TRYING [4]
% 0.23/0.46 TRYING [5]
% 0.23/0.52 TRYING [5]
% 0.23/0.55 TRYING [6]
% 1.97/0.68 TRYING [6]
% 2.60/0.74 TRYING [7]
% 5.10/1.15 TRYING [8]
% 5.59/1.16 TRYING [7]
% 7.79/1.49 TRYING [1]
% 7.79/1.49 TRYING [2]
% 7.79/1.49 TRYING [3]
% 7.79/1.50 TRYING [4]
% 8.12/1.53 TRYING [5]
% 8.88/1.63 TRYING [6]
% 10.27/1.86 TRYING [7]
% 13.59/2.35 TRYING [9]
% 14.37/2.49 TRYING [8]
% 26.53/4.14 % (8935)First to succeed.
% 26.53/4.15 % (8935)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8932"
% 26.53/4.15 % (8935)Refutation found. Thanks to Tanya!
% 26.53/4.15 % SZS status Unsatisfiable for theBenchmark
% 26.53/4.15 % SZS output start Proof for theBenchmark
% See solution above
% 26.53/4.15 % (8935)------------------------------
% 26.53/4.15 % (8935)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 26.53/4.15 % (8935)Termination reason: Refutation
% 26.53/4.15
% 26.53/4.15 % (8935)Memory used [KB]: 53879
% 26.53/4.15 % (8935)Time elapsed: 3.753 s
% 26.53/4.15 % (8935)Instructions burned: 17748 (million)
% 26.53/4.15 % (8932)Success in time 3.726 s
%------------------------------------------------------------------------------