TSTP Solution File: HAL006+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : HAL006+1 : TPTP v8.1.2. Released v2.6.0.
% 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 : Tue Apr 30 12:09:42 EDT 2024
% Result : Theorem 142.86s 20.68s
% Output : Refutation 142.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 23 unt; 0 def)
% Number of atoms : 200 ( 66 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 196 ( 61 ~; 53 |; 65 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 140 ( 110 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1298189,plain,
$false,
inference(subsumption_resolution,[],[f1298188,f129441]) ).
fof(f129441,plain,
sK7 != apply(g,subtract(b,sK10(sK7),sK18(sK11(sK7),g,b))),
inference(unit_resulting_resolution,[],[f226,f79292,f126]) ).
fof(f126,plain,
! [X2,X1] :
( ~ element(X2,b)
| apply(g,subtract(b,X1,X2)) != sK7
| ~ element(X1,b) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ! [X1,X2] :
( apply(g,subtract(b,X1,X2)) != sK7
| ~ element(X2,b)
| ~ element(X1,b) )
& element(sK7,e) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f50,f89]) ).
fof(f89,plain,
( ? [X0] :
( ! [X1,X2] :
( apply(g,subtract(b,X1,X2)) != X0
| ~ element(X2,b)
| ~ element(X1,b) )
& element(X0,e) )
=> ( ! [X2,X1] :
( apply(g,subtract(b,X1,X2)) != sK7
| ~ element(X2,b)
| ~ element(X1,b) )
& element(sK7,e) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
? [X0] :
( ! [X1,X2] :
( apply(g,subtract(b,X1,X2)) != X0
| ~ element(X2,b)
| ~ element(X1,b) )
& element(X0,e) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
~ ! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( apply(g,subtract(b,X1,X2)) = X0
& element(X2,b)
& element(X1,b) ) ),
inference(rectify,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X18] :
( element(X18,e)
=> ? [X20,X23] :
( apply(g,subtract(b,X20,X23)) = X18
& element(X23,b)
& element(X20,b) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X18] :
( element(X18,e)
=> ? [X20,X23] :
( apply(g,subtract(b,X20,X23)) = X18
& element(X23,b)
& element(X20,b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma12) ).
fof(f79292,plain,
element(sK18(sK11(sK7),g,b),b),
inference(unit_resulting_resolution,[],[f79290,f181]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| element(sK18(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ! [X3] :
( apply(X1,X3) != X0
| ~ element(X3,X2) ) )
& ( ( apply(X1,sK18(X0,X1,X2)) = X0
& element(sK18(X0,X1,X2),X2) )
| ~ sP6(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f114,f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X1,X4) = X0
& element(X4,X2) )
=> ( apply(X1,sK18(X0,X1,X2)) = X0
& element(sK18(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ! [X3] :
( apply(X1,X3) != X0
| ~ element(X3,X2) ) )
& ( ? [X4] :
( apply(X1,X4) = X0
& element(X4,X2) )
| ~ sP6(X0,X1,X2) ) ),
inference(rectify,[],[f113]) ).
fof(f113,plain,
! [X5,X0,X2] :
( ( sP6(X5,X0,X2)
| ! [X6] :
( apply(X0,X6) != X5
| ~ element(X6,X2) ) )
& ( ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) )
| ~ sP6(X5,X0,X2) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X5,X0,X2] :
( sP6(X5,X0,X2)
<=> ? [X6] :
( apply(X0,X6) = X5
& element(X6,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f79290,plain,
sP6(sK11(sK7),g,b),
inference(superposition,[],[f6274,f2934]) ).
fof(f2934,plain,
sK11(sK7) = apply(g,apply(alpha,sK12(sK7))),
inference(unit_resulting_resolution,[],[f220,f155]) ).
fof(f155,plain,
! [X0] :
( ~ sP1(X0)
| sK11(X0) = apply(g,apply(alpha,sK12(X0))) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( sK11(X0) = apply(g,apply(alpha,sK12(X0)))
& sK11(X0) = apply(gamma,apply(f,sK12(X0)))
& element(sK12(X0),a)
& sK11(X0) = subtract(e,apply(g,sK10(X0)),X0)
& element(sK11(X0),e)
& element(sK10(X0),b) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f94,f95]) ).
fof(f95,plain,
! [X0] :
( ? [X1,X2,X3] :
( apply(g,apply(alpha,X3)) = X2
& apply(gamma,apply(f,X3)) = X2
& element(X3,a)
& subtract(e,apply(g,X1),X0) = X2
& element(X2,e)
& element(X1,b) )
=> ( sK11(X0) = apply(g,apply(alpha,sK12(X0)))
& sK11(X0) = apply(gamma,apply(f,sK12(X0)))
& element(sK12(X0),a)
& sK11(X0) = subtract(e,apply(g,sK10(X0)),X0)
& element(sK11(X0),e)
& element(sK10(X0),b) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0] :
( ? [X1,X2,X3] :
( apply(g,apply(alpha,X3)) = X2
& apply(gamma,apply(f,X3)) = X2
& element(X3,a)
& subtract(e,apply(g,X1),X0) = X2
& element(X2,e)
& element(X1,b) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ? [X1,X2,X3] :
( apply(g,apply(alpha,X3)) = X2
& apply(gamma,apply(f,X3)) = X2
& element(X3,a)
& subtract(e,apply(g,X1),X0) = X2
& element(X2,e)
& element(X1,b) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f220,plain,
sP1(sK7),
inference(unit_resulting_resolution,[],[f125,f156]) ).
fof(f156,plain,
! [X0] :
( ~ element(X0,e)
| sP1(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( sP1(X0)
| ~ element(X0,e) ),
inference(definition_folding,[],[f52,f79]) ).
fof(f52,plain,
! [X0] :
( ? [X1,X2,X3] :
( apply(g,apply(alpha,X3)) = X2
& apply(gamma,apply(f,X3)) = X2
& element(X3,a)
& subtract(e,apply(g,X1),X0) = X2
& element(X2,e)
& element(X1,b) )
| ~ element(X0,e) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( element(X0,e)
=> ? [X1,X2,X3] :
( apply(g,apply(alpha,X3)) = X2
& apply(gamma,apply(f,X3)) = X2
& element(X3,a)
& subtract(e,apply(g,X1),X0) = X2
& element(X2,e)
& element(X1,b) ) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X18] :
( element(X18,e)
=> ? [X20,X21,X22] :
( apply(g,apply(alpha,X22)) = X21
& apply(gamma,apply(f,X22)) = X21
& element(X22,a)
& subtract(e,apply(g,X20),X18) = X21
& element(X21,e)
& element(X20,b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma8) ).
fof(f125,plain,
element(sK7,e),
inference(cnf_transformation,[],[f90]) ).
fof(f6274,plain,
! [X0] : sP6(apply(X0,apply(alpha,sK12(sK7))),X0,b),
inference(unit_resulting_resolution,[],[f5902,f193]) ).
fof(f193,plain,
! [X2,X3,X1] :
( ~ element(X3,X2)
| sP6(apply(X1,X3),X1,X2) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X1,X2)
| apply(X1,X3) != X0
| ~ element(X3,X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f5902,plain,
element(apply(alpha,sK12(sK7)),b),
inference(unit_resulting_resolution,[],[f138,f266,f158]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1) ) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',morphism) ).
fof(f266,plain,
element(sK12(sK7),a),
inference(unit_resulting_resolution,[],[f220,f153]) ).
fof(f153,plain,
! [X0] :
( ~ sP1(X0)
| element(sK12(X0),a) ),
inference(cnf_transformation,[],[f96]) ).
fof(f138,plain,
morphism(alpha,a,b),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alpha_morphism) ).
fof(f226,plain,
element(sK10(sK7),b),
inference(unit_resulting_resolution,[],[f220,f150]) ).
fof(f150,plain,
! [X0] :
( ~ sP1(X0)
| element(sK10(X0),b) ),
inference(cnf_transformation,[],[f96]) ).
fof(f1298188,plain,
sK7 = apply(g,subtract(b,sK10(sK7),sK18(sK11(sK7),g,b))),
inference(forward_demodulation,[],[f1298187,f534668]) ).
fof(f534668,plain,
sK7 = subtract(e,apply(g,sK10(sK7)),sK11(sK7)),
inference(forward_demodulation,[],[f381293,f5244]) ).
fof(f5244,plain,
sK11(sK7) = subtract(e,apply(g,sK10(sK7)),sK7),
inference(unit_resulting_resolution,[],[f220,f152]) ).
fof(f152,plain,
! [X0] :
( ~ sP1(X0)
| sK11(X0) = subtract(e,apply(g,sK10(X0)),X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f381293,plain,
sK7 = subtract(e,apply(g,sK10(sK7)),subtract(e,apply(g,sK10(sK7)),sK7)),
inference(unit_resulting_resolution,[],[f5732,f125,f165]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> subtract(X1,X4,subtract(X1,X4,X5)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_cancellation) ).
fof(f5732,plain,
element(apply(g,sK10(sK7)),e),
inference(unit_resulting_resolution,[],[f141,f226,f158]) ).
fof(f141,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_morphism) ).
fof(f1298187,plain,
subtract(e,apply(g,sK10(sK7)),sK11(sK7)) = apply(g,subtract(b,sK10(sK7),sK18(sK11(sK7),g,b))),
inference(forward_demodulation,[],[f1277550,f79291]) ).
fof(f79291,plain,
sK11(sK7) = apply(g,sK18(sK11(sK7),g,b)),
inference(unit_resulting_resolution,[],[f79290,f182]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| apply(X1,sK18(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f1277550,plain,
apply(g,subtract(b,sK10(sK7),sK18(sK11(sK7),g,b))) = subtract(e,apply(g,sK10(sK7)),apply(g,sK18(sK11(sK7),g,b))),
inference(unit_resulting_resolution,[],[f141,f226,f79292,f160]) ).
fof(f160,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X4,X1)
& element(X3,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> apply(X0,subtract(X1,X4,X5)) = subtract(X2,apply(X0,X4),apply(X0,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_distribution) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HAL006+1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 30 03:24:05 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % (17475)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.35 % (17479)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 TRYING [1]
% 0.14/0.36 TRYING [2]
% 0.14/0.36 % (17478)WARNING: value z3 for option sas not known
% 0.14/0.36 % (17476)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (17477)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36 % (17478)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)
% 0.14/0.36 % (17480)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)
% 0.14/0.36 % (17481)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)
% 0.14/0.36 % (17482)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)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [3]
% 0.14/0.39 TRYING [3]
% 0.20/0.49 TRYING [4]
% 0.20/0.53 TRYING [4]
% 6.39/1.27 TRYING [5]
% 6.87/1.36 TRYING [5]
% 7.88/1.46 TRYING [1]
% 7.88/1.47 TRYING [2]
% 7.88/1.48 TRYING [3]
% 8.52/1.60 TRYING [4]
% 16.74/2.74 TRYING [5]
% 46.90/7.05 TRYING [6]
% 60.65/9.02 TRYING [6]
% 78.61/11.57 TRYING [6]
% 142.33/20.61 % (17482)First to succeed.
% 142.86/20.68 % (17482)Refutation found. Thanks to Tanya!
% 142.86/20.68 % SZS status Theorem for theBenchmark
% 142.86/20.68 % SZS output start Proof for theBenchmark
% See solution above
% 142.86/20.68 % (17482)------------------------------
% 142.86/20.68 % (17482)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 142.86/20.68 % (17482)Termination reason: Refutation
% 142.86/20.68
% 142.86/20.68 % (17482)Memory used [KB]: 639536
% 142.86/20.68 % (17482)Time elapsed: 20.250 s
% 142.86/20.68 % (17482)Instructions burned: 75582 (million)
% 142.86/20.68 % (17482)------------------------------
% 142.86/20.68 % (17482)------------------------------
% 142.86/20.68 % (17475)Success in time 20.151 s
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