TSTP Solution File: LCL145-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL145-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n031.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 : Sun May 5 07:44:11 EDT 2024
% Result : Unsatisfiable 3.59s 0.89s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 76 unt; 0 def)
% Number of atoms : 82 ( 73 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22189,plain,
$false,
inference(trivial_inequality_removal,[],[f22118]) ).
fof(f22118,plain,
not(big_V(x,y)) != not(big_V(x,y)),
inference(superposition,[],[f9,f7854]) ).
fof(f7854,plain,
! [X0,X1] : not(big_V(X1,X0)) = big_hat(not(X1),not(X0)),
inference(superposition,[],[f2985,f2740]) ).
fof(f2740,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f2739,f2356]) ).
fof(f2356,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(forward_demodulation,[],[f2318,f1271]) ).
fof(f1271,plain,
! [X0] : big_V(X0,not(truth)) = X0,
inference(forward_demodulation,[],[f1246,f1]) ).
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f1246,plain,
! [X0] : implies(truth,X0) = big_V(X0,not(truth)),
inference(superposition,[],[f10,f1054]) ).
fof(f1054,plain,
! [X0] : truth = implies(not(truth),X0),
inference(superposition,[],[f1043,f1]) ).
fof(f1043,plain,
! [X0] : truth = implies(truth,implies(not(truth),X0)),
inference(resolution,[],[f1018,f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ ordered(X0,X1)
| truth = implies(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition1) ).
fof(f1018,plain,
! [X0] : ordered(truth,implies(not(truth),X0)),
inference(superposition,[],[f835,f126]) ).
fof(f126,plain,
! [X0] : big_V(implies(not(X0),not(truth)),X0) = X0,
inference(forward_demodulation,[],[f121,f1]) ).
fof(f121,plain,
! [X0] : implies(truth,X0) = big_V(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f5,f96]) ).
fof(f96,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f4,f1]) ).
fof(f4,axiom,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).
fof(f835,plain,
! [X2,X0,X1] : ordered(truth,implies(X0,big_V(implies(X1,X0),X2))),
inference(superposition,[],[f815,f439]) ).
fof(f439,plain,
! [X0,X1] : truth = implies(X0,implies(X1,X0)),
inference(superposition,[],[f277,f1]) ).
fof(f277,plain,
! [X0,X1] : truth = implies(truth,implies(X0,implies(X1,X0))),
inference(backward_demodulation,[],[f166,f247]) ).
fof(f247,plain,
! [X0] : truth = implies(X0,truth),
inference(backward_demodulation,[],[f208,f223]) ).
fof(f223,plain,
! [X0] : truth = implies(X0,X0),
inference(backward_demodulation,[],[f14,f213]) ).
fof(f213,plain,
! [X0] : truth = big_V(truth,X0),
inference(superposition,[],[f197,f1]) ).
fof(f197,plain,
! [X0,X1] : truth = implies(X0,big_V(X0,X1)),
inference(forward_demodulation,[],[f196,f5]) ).
fof(f196,plain,
! [X0,X1] : truth = implies(X0,implies(implies(X0,X1),X1)),
inference(forward_demodulation,[],[f156,f1]) ).
fof(f156,plain,
! [X0,X1] : truth = implies(X0,implies(implies(X0,X1),implies(truth,X1))),
inference(superposition,[],[f2,f1]) ).
fof(f2,axiom,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f14,plain,
! [X0] : big_V(truth,X0) = implies(X0,X0),
inference(superposition,[],[f5,f1]) ).
fof(f208,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f197,f20]) ).
fof(f20,plain,
! [X0] : implies(X0,X0) = big_V(X0,truth),
inference(superposition,[],[f10,f1]) ).
fof(f166,plain,
! [X0,X1] : truth = implies(implies(X1,truth),implies(X0,implies(X1,X0))),
inference(superposition,[],[f2,f1]) ).
fof(f815,plain,
! [X2,X0,X1] : ordered(implies(X2,X0),implies(X2,big_V(X0,X1))),
inference(forward_demodulation,[],[f780,f1]) ).
fof(f780,plain,
! [X2,X0,X1] : ordered(implies(X2,X0),implies(truth,implies(X2,big_V(X0,X1)))),
inference(superposition,[],[f193,f197]) ).
fof(f193,plain,
! [X2,X0,X1] : ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(trivial_inequality_removal,[],[f191]) ).
fof(f191,plain,
! [X2,X0,X1] :
( truth != truth
| ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) ),
inference(superposition,[],[f8,f2]) ).
fof(f8,axiom,
! [X0,X1] :
( truth != implies(X0,X1)
| ordered(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition2) ).
fof(f10,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X1,X0),
inference(forward_demodulation,[],[f3,f5]) ).
fof(f3,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f2318,plain,
! [X0] : implies(X0,not(truth)) = big_V(not(X0),not(truth)),
inference(superposition,[],[f5,f2181]) ).
fof(f2181,plain,
! [X0] : implies(not(X0),not(truth)) = X0,
inference(forward_demodulation,[],[f2180,f125]) ).
fof(f125,plain,
! [X0] : big_V(X0,implies(not(X0),not(truth))) = X0,
inference(forward_demodulation,[],[f120,f1]) ).
fof(f120,plain,
! [X0] : implies(truth,X0) = big_V(X0,implies(not(X0),not(truth))),
inference(superposition,[],[f10,f96]) ).
fof(f2180,plain,
! [X0] : implies(not(X0),not(truth)) = big_V(X0,implies(not(X0),not(truth))),
inference(forward_demodulation,[],[f2150,f1]) ).
fof(f2150,plain,
! [X0] : big_V(X0,implies(not(X0),not(truth))) = implies(truth,implies(not(X0),not(truth))),
inference(superposition,[],[f5,f2112]) ).
fof(f2112,plain,
! [X0] : truth = implies(X0,implies(not(X0),not(truth))),
inference(forward_demodulation,[],[f2062,f244]) ).
fof(f244,plain,
! [X0] : truth = big_V(X0,truth),
inference(backward_demodulation,[],[f20,f223]) ).
fof(f2062,plain,
! [X0] : implies(X0,implies(not(X0),not(truth))) = big_V(implies(X0,implies(not(X0),not(truth))),truth),
inference(superposition,[],[f109,f1270]) ).
fof(f1270,plain,
! [X0] : truth = implies(not(implies(X0,not(truth))),X0),
inference(backward_demodulation,[],[f1227,f1269]) ).
fof(f1269,plain,
! [X0] : big_V(not(truth),X0) = X0,
inference(forward_demodulation,[],[f1244,f1]) ).
fof(f1244,plain,
! [X0] : implies(truth,X0) = big_V(not(truth),X0),
inference(superposition,[],[f5,f1054]) ).
fof(f1227,plain,
! [X0] : truth = implies(not(implies(X0,not(truth))),big_V(not(truth),X0)),
inference(forward_demodulation,[],[f1212,f1]) ).
fof(f1212,plain,
! [X0] : truth = implies(implies(truth,not(implies(X0,not(truth)))),big_V(not(truth),X0)),
inference(superposition,[],[f97,f1081]) ).
fof(f1081,plain,
truth = not(not(truth)),
inference(backward_demodulation,[],[f533,f1054]) ).
fof(f533,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(forward_demodulation,[],[f516,f1]) ).
fof(f516,plain,
implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))),
inference(superposition,[],[f499,f115]) ).
fof(f115,plain,
truth = big_V(not(truth),not(not(truth))),
inference(superposition,[],[f96,f10]) ).
fof(f499,plain,
! [X0,X1] : implies(X0,X1) = implies(big_V(X0,X1),X1),
inference(backward_demodulation,[],[f22,f498]) ).
fof(f498,plain,
! [X0,X1] : implies(X1,X0) = big_V(X0,implies(X1,X0)),
inference(forward_demodulation,[],[f490,f1]) ).
fof(f490,plain,
! [X0,X1] : big_V(X0,implies(X1,X0)) = implies(truth,implies(X1,X0)),
inference(superposition,[],[f5,f439]) ).
fof(f22,plain,
! [X0,X1] : implies(big_V(X0,X1),X1) = big_V(X1,implies(X0,X1)),
inference(superposition,[],[f10,f5]) ).
fof(f97,plain,
! [X0,X1] : truth = implies(implies(not(X1),not(implies(X0,X1))),big_V(X1,X0)),
inference(superposition,[],[f4,f10]) ).
fof(f109,plain,
! [X0,X1] : implies(X1,X0) = big_V(implies(X1,X0),implies(not(X0),not(X1))),
inference(forward_demodulation,[],[f102,f1]) ).
fof(f102,plain,
! [X0,X1] : big_V(implies(X1,X0),implies(not(X0),not(X1))) = implies(truth,implies(X1,X0)),
inference(superposition,[],[f10,f4]) ).
fof(f2739,plain,
! [X0] : not(implies(X0,not(truth))) = X0,
inference(forward_demodulation,[],[f2692,f1269]) ).
fof(f2692,plain,
! [X0] : not(implies(X0,not(truth))) = big_V(not(truth),X0),
inference(superposition,[],[f2356,f10]) ).
fof(f2985,plain,
! [X0,X1] : not(big_V(X0,not(X1))) = big_hat(not(X0),X1),
inference(superposition,[],[f2407,f2741]) ).
fof(f2741,plain,
! [X0] : big_hat(X0,X0) = X0,
inference(backward_demodulation,[],[f392,f2740]) ).
fof(f392,plain,
! [X0] : not(not(X0)) = big_hat(X0,X0),
inference(superposition,[],[f42,f261]) ).
fof(f261,plain,
! [X0] : big_V(X0,X0) = X0,
inference(forward_demodulation,[],[f249,f1]) ).
fof(f249,plain,
! [X0] : implies(truth,X0) = big_V(X0,X0),
inference(backward_demodulation,[],[f31,f244]) ).
fof(f31,plain,
! [X0] : big_V(X0,X0) = implies(big_V(X0,truth),X0),
inference(superposition,[],[f10,f20]) ).
fof(f42,plain,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X1),not(X0))),
inference(superposition,[],[f6,f24]) ).
fof(f24,plain,
! [X0,X1] : big_V(X0,X1) = big_V(X1,X0),
inference(superposition,[],[f10,f5]) ).
fof(f6,axiom,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).
fof(f2407,plain,
! [X2,X0,X1] : not(big_V(big_hat(X0,X1),not(X2))) = big_hat(not(big_hat(X0,X1)),X2),
inference(backward_demodulation,[],[f28,f2393]) ).
fof(f2393,plain,
! [X0,X1] : big_V(not(X0),not(X1)) = not(big_hat(X0,X1)),
inference(backward_demodulation,[],[f2300,f2356]) ).
fof(f2300,plain,
! [X0,X1] : big_V(not(X0),not(X1)) = implies(big_hat(X0,X1),not(truth)),
inference(superposition,[],[f2181,f6]) ).
fof(f28,plain,
! [X2,X0,X1] : big_hat(big_V(not(X0),not(X1)),X2) = not(big_V(big_hat(X0,X1),not(X2))),
inference(superposition,[],[f6,f6]) ).
fof(f9,axiom,
not(big_V(x,y)) != big_hat(not(x),not(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL145-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 14:01:47 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (6461)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (6464)WARNING: value z3 for option sas not known
% 0.21/0.38 % (6462)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (6465)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (6463)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (6466)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)
% 0.21/0.38 % (6467)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)
% 0.21/0.38 % (6464)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)
% 0.21/0.38 % (6468)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)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [4]
% 0.21/0.39 TRYING [3]
% 0.21/0.41 TRYING [5]
% 0.21/0.42 TRYING [4]
% 0.21/0.48 TRYING [6]
% 1.51/0.60 TRYING [5]
% 3.59/0.89 % (6467)First to succeed.
% 3.59/0.89 % (6467)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6461"
% 3.59/0.89 % (6467)Refutation found. Thanks to Tanya!
% 3.59/0.89 % SZS status Unsatisfiable for theBenchmark
% 3.59/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/0.89 % (6467)------------------------------
% 3.59/0.89 % (6467)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.59/0.89 % (6467)Termination reason: Refutation
% 3.59/0.89
% 3.59/0.89 % (6467)Memory used [KB]: 6380
% 3.59/0.89 % (6467)Time elapsed: 0.509 s
% 3.59/0.89 % (6467)Instructions burned: 922 (million)
% 3.59/0.89 % (6461)Success in time 0.516 s
%------------------------------------------------------------------------------