TSTP Solution File: ALG073+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n016.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 : Wed Aug 31 15:42:29 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 15 unt; 0 def)
% Number of atoms : 217 ( 78 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 242 ( 84 ~; 70 |; 53 &)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 75 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f157,plain,
$false,
inference(avatar_sat_refutation,[],[f85,f90,f156]) ).
fof(f156,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f155,plain,
( $false
| ~ spl2_3 ),
inference(subsumption_resolution,[],[f154,f27]) ).
fof(f27,plain,
op1(sK0,sK1) != sK0,
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( sK0 = op1(sK1,sK1)
& op1(sK0,sK1) != sK0
& sK1 = op1(sK0,sK0)
& sorti1(sK1)
& sorti1(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f3,f15,f14]) ).
fof(f14,plain,
( ? [X0] :
( ? [X1] :
( op1(X1,X1) = X0
& op1(X0,X1) != X0
& op1(X0,X0) = X1
& sorti1(X1) )
& sorti1(X0) )
=> ( ? [X1] :
( op1(X1,X1) = sK0
& op1(sK0,X1) != sK0
& op1(sK0,sK0) = X1
& sorti1(X1) )
& sorti1(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X1] :
( op1(X1,X1) = sK0
& op1(sK0,X1) != sK0
& op1(sK0,sK0) = X1
& sorti1(X1) )
=> ( sK0 = op1(sK1,sK1)
& op1(sK0,sK1) != sK0
& sK1 = op1(sK0,sK0)
& sorti1(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f3,axiom,
? [X0] :
( ? [X1] :
( op1(X1,X1) = X0
& op1(X0,X1) != X0
& op1(X0,X0) = X1
& sorti1(X1) )
& sorti1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f154,plain,
( op1(sK0,sK1) = sK0
| ~ spl2_3 ),
inference(forward_demodulation,[],[f153,f34]) ).
fof(f34,plain,
sK0 = j(h(sK0)),
inference(resolution,[],[f21,f24]) ).
fof(f24,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f21,plain,
! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ! [X0] :
( ! [X1] :
( j(op2(X0,X1)) = op1(j(X0),j(X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) )
& ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( ~ sorti1(X3)
| sorti2(h(X3)) )
& ! [X4] :
( ~ sorti2(X4)
| sorti1(j(X4)) )
& ! [X5] :
( h(j(X5)) = X5
| ~ sorti2(X5) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) ) ),
inference(rectify,[],[f12]) ).
fof(f12,plain,
( ! [X2] :
( ! [X3] :
( op1(j(X2),j(X3)) = j(op2(X2,X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X4] :
( ! [X5] :
( op2(h(X4),h(X5)) = h(op1(X4,X5))
| ~ sorti1(X5) )
| ~ sorti1(X4) ) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
( ! [X4] :
( ! [X5] :
( op2(h(X4),h(X5)) = h(op1(X4,X5))
| ~ sorti1(X5) )
| ~ sorti1(X4) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X2] :
( ! [X3] :
( op1(j(X2),j(X3)) = j(op2(X2,X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X4] :
( sorti1(X4)
=> ! [X5] :
( sorti1(X5)
=> op2(h(X4),h(X5)) = h(op1(X4,X5)) ) )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X2] :
( sorti2(X2)
=> ! [X3] :
( sorti2(X3)
=> op1(j(X2),j(X3)) = j(op2(X2,X3)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f153,plain,
( op1(sK0,sK1) = j(h(sK0))
| ~ spl2_3 ),
inference(forward_demodulation,[],[f151,f133]) ).
fof(f133,plain,
( h(sK0) = h(op1(sK0,sK1))
| ~ spl2_3 ),
inference(backward_demodulation,[],[f64,f132]) ).
fof(f132,plain,
( op2(h(sK0),h(sK1)) = h(sK0)
| ~ spl2_3 ),
inference(subsumption_resolution,[],[f131,f84]) ).
fof(f84,plain,
( sorti2(h(sK1))
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f82,plain,
( spl2_3
<=> sorti2(h(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f131,plain,
( ~ sorti2(h(sK1))
| op2(h(sK0),h(sK1)) = h(sK0) ),
inference(subsumption_resolution,[],[f129,f61]) ).
fof(f61,plain,
h(sK1) = op2(h(sK0),h(sK0)),
inference(forward_demodulation,[],[f59,f26]) ).
fof(f26,plain,
sK1 = op1(sK0,sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f59,plain,
h(op1(sK0,sK0)) = op2(h(sK0),h(sK0)),
inference(resolution,[],[f47,f24]) ).
fof(f47,plain,
! [X5] :
( ~ sorti1(X5)
| h(op1(X5,sK0)) = op2(h(X5),h(sK0)) ),
inference(resolution,[],[f17,f24]) ).
fof(f17,plain,
! [X6,X7] :
( ~ sorti1(X7)
| ~ sorti1(X6)
| h(op1(X6,X7)) = op2(h(X6),h(X7)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f129,plain,
( h(sK1) != op2(h(sK0),h(sK0))
| op2(h(sK0),h(sK1)) = h(sK0)
| ~ sorti2(h(sK1)) ),
inference(superposition,[],[f32,f66]) ).
fof(f66,plain,
op2(h(sK1),h(sK1)) = h(sK0),
inference(forward_demodulation,[],[f65,f28]) ).
fof(f28,plain,
sK0 = op1(sK1,sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f65,plain,
op2(h(sK1),h(sK1)) = h(op1(sK1,sK1)),
inference(resolution,[],[f48,f25]) ).
fof(f25,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f48,plain,
! [X6] :
( ~ sorti1(X6)
| op2(h(X6),h(sK1)) = h(op1(X6,sK1)) ),
inference(resolution,[],[f17,f25]) ).
fof(f32,plain,
! [X1] :
( op2(op2(X1,X1),op2(X1,X1)) != X1
| ~ sorti2(X1)
| op2(X1,X1) = op2(op2(X1,X1),X1) ),
inference(subsumption_resolution,[],[f31,f23]) ).
fof(f23,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f31,plain,
! [X1] :
( ~ sorti2(op2(X1,X1))
| op2(op2(X1,X1),op2(X1,X1)) != X1
| ~ sorti2(X1)
| op2(X1,X1) = op2(op2(X1,X1),X1) ),
inference(equality_resolution,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ? [X0] :
( ? [X1] :
( op2(X1,X1) = X0
& sorti2(X1)
& op2(X0,X0) = X1
& op2(X0,X1) != X0 )
& sorti2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f64,plain,
op2(h(sK0),h(sK1)) = h(op1(sK0,sK1)),
inference(resolution,[],[f48,f24]) ).
fof(f151,plain,
op1(sK0,sK1) = j(h(op1(sK0,sK1))),
inference(resolution,[],[f100,f25]) ).
fof(f100,plain,
! [X5] :
( ~ sorti1(X5)
| op1(sK0,X5) = j(h(op1(sK0,X5))) ),
inference(resolution,[],[f40,f24]) ).
fof(f40,plain,
! [X0,X1] :
( ~ sorti1(X1)
| j(h(op1(X1,X0))) = op1(X1,X0)
| ~ sorti1(X0) ),
inference(resolution,[],[f29,f21]) ).
fof(f29,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] :
( ! [X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1)) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f90,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f89]) ).
fof(f89,plain,
( $false
| spl2_2 ),
inference(subsumption_resolution,[],[f88,f24]) ).
fof(f88,plain,
( ~ sorti1(sK0)
| spl2_2 ),
inference(resolution,[],[f79,f20]) ).
fof(f20,plain,
! [X3] :
( sorti2(h(X3))
| ~ sorti1(X3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f79,plain,
( ~ sorti2(h(sK0))
| spl2_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f77,plain,
( spl2_2
<=> sorti2(h(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f85,plain,
( spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f69,f77,f82]) ).
fof(f69,plain,
( ~ sorti2(h(sK0))
| sorti2(h(sK1)) ),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f67,plain,
( ~ sorti2(h(sK0))
| sorti2(h(sK1))
| ~ sorti2(h(sK0)) ),
inference(superposition,[],[f23,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 15:15:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.48 % (32466)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.49 % (32481)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.50 % (32461)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (32479)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.50 % (32481)First to succeed.
% 0.19/0.50 % (32465)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.50 % (32473)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.50 % (32471)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.50 % (32481)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (32481)------------------------------
% 0.19/0.50 % (32481)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (32481)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (32481)Termination reason: Refutation
% 0.19/0.50
% 0.19/0.50 % (32481)Memory used [KB]: 5500
% 0.19/0.50 % (32481)Time elapsed: 0.110 s
% 0.19/0.50 % (32481)Instructions burned: 7 (million)
% 0.19/0.50 % (32481)------------------------------
% 0.19/0.50 % (32481)------------------------------
% 0.19/0.50 % (32456)Success in time 0.164 s
%------------------------------------------------------------------------------