TSTP Solution File: ALG073+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---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_uns --cores 0 -t %d %s
% Computer : n025.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 15:39:22 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 21 unt; 0 def)
% Number of atoms : 199 ( 88 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 219 ( 75 ~; 61 |; 53 &)
% ( 1 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 59 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f135,plain,
$false,
inference(avatar_sat_refutation,[],[f86,f134]) ).
fof(f134,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f133,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[],[f132,f19]) ).
fof(f19,plain,
op1(sK0,sK1) != sK0,
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( sorti1(sK0)
& sorti1(sK1)
& op1(sK0,sK1) != sK0
& sK0 = op1(sK1,sK1)
& op1(sK0,sK0) = sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f3,f14,f13]) ).
fof(f13,plain,
( ? [X0] :
( sorti1(X0)
& ? [X1] :
( sorti1(X1)
& op1(X0,X1) != X0
& op1(X1,X1) = X0
& op1(X0,X0) = X1 ) )
=> ( sorti1(sK0)
& ? [X1] :
( sorti1(X1)
& op1(sK0,X1) != sK0
& op1(X1,X1) = sK0
& op1(sK0,sK0) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ? [X1] :
( sorti1(X1)
& op1(sK0,X1) != sK0
& op1(X1,X1) = sK0
& op1(sK0,sK0) = X1 )
=> ( sorti1(sK1)
& op1(sK0,sK1) != sK0
& sK0 = op1(sK1,sK1)
& op1(sK0,sK0) = sK1 ) ),
introduced(choice_axiom,[]) ).
fof(f3,axiom,
? [X0] :
( sorti1(X0)
& ? [X1] :
( sorti1(X1)
& op1(X0,X1) != X0
& op1(X1,X1) = X0
& op1(X0,X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f132,plain,
( op1(sK0,sK1) = sK0
| ~ spl2_1 ),
inference(forward_demodulation,[],[f130,f59]) ).
fof(f59,plain,
j(h(sK0)) = sK0,
inference(unit_resulting_resolution,[],[f21,f28]) ).
fof(f28,plain,
! [X3] :
( ~ sorti1(X3)
| j(h(X3)) = X3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X1] :
( ! [X2] :
( ~ sorti1(X2)
| op2(h(X1),h(X2)) = h(op1(X1,X2)) )
| ~ sorti1(X1) )
& ! [X3] :
( ~ sorti1(X3)
| j(h(X3)) = X3 )
& ! [X4] :
( ~ sorti2(X4)
| sorti1(j(X4)) )
& ! [X5] :
( ! [X6] :
( ~ sorti2(X6)
| j(op2(X5,X6)) = op1(j(X5),j(X6)) )
| ~ sorti2(X5) )
& ! [X7] :
( h(j(X7)) = X7
| ~ sorti2(X7) ) ),
inference(rectify,[],[f10]) ).
fof(f10,plain,
( ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X4] :
( ! [X5] :
( ~ sorti1(X5)
| h(op1(X4,X5)) = op2(h(X4),h(X5)) )
| ~ sorti1(X4) )
& ! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X6] :
( ! [X7] :
( ~ sorti2(X7)
| j(op2(X6,X7)) = op1(j(X6),j(X7)) )
| ~ sorti2(X6) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) ) ),
inference(flattening,[],[f9]) ).
fof(f9,plain,
( ! [X4] :
( ! [X5] :
( ~ sorti1(X5)
| h(op1(X4,X5)) = op2(h(X4),h(X5)) )
| ~ sorti1(X4) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 )
& ! [X6] :
( ! [X7] :
( ~ sorti2(X7)
| j(op2(X6,X7)) = op1(j(X6),j(X7)) )
| ~ sorti2(X6) )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X4] :
( sorti1(X4)
=> ! [X5] :
( sorti1(X5)
=> h(op1(X4,X5)) = op2(h(X4),h(X5)) ) )
& ! [X3] :
( sorti2(X3)
=> h(j(X3)) = X3 )
& ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X6] :
( sorti2(X6)
=> ! [X7] :
( sorti2(X7)
=> j(op2(X6,X7)) = op1(j(X6),j(X7)) ) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f21,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f130,plain,
( j(h(sK0)) = op1(sK0,sK1)
| ~ spl2_1 ),
inference(backward_demodulation,[],[f122,f129]) ).
fof(f129,plain,
( h(sK0) = h(op1(sK0,sK1))
| ~ spl2_1 ),
inference(backward_demodulation,[],[f74,f128]) ).
fof(f128,plain,
( h(sK0) = op2(h(sK0),h(sK1))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f127,f87]) ).
fof(f87,plain,
( op2(h(sK0),h(sK0)) = h(sK1)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f52,f80]) ).
fof(f80,plain,
h(sK0) = op2(h(sK1),h(sK1)),
inference(forward_demodulation,[],[f75,f18]) ).
fof(f18,plain,
sK0 = op1(sK1,sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f75,plain,
h(op1(sK1,sK1)) = op2(h(sK1),h(sK1)),
inference(unit_resulting_resolution,[],[f20,f20,f29]) ).
fof(f29,plain,
! [X2,X1] :
( ~ sorti1(X2)
| op2(h(X1),h(X2)) = h(op1(X1,X2))
| ~ sorti1(X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f20,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f52,plain,
( op2(op2(h(sK1),h(sK1)),op2(h(sK1),h(sK1))) = h(sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f51,plain,
( spl2_1
<=> op2(op2(h(sK1),h(sK1)),op2(h(sK1),h(sK1))) = h(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f127,plain,
( h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
| ~ spl2_1 ),
inference(subsumption_resolution,[],[f126,f80]) ).
fof(f126,plain,
( h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
| h(sK0) != op2(h(sK1),h(sK1))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f125,f87]) ).
fof(f125,plain,
( h(sK0) != op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0)))
| h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
| ~ spl2_1 ),
inference(subsumption_resolution,[],[f124,f35]) ).
fof(f35,plain,
sorti2(h(sK1)),
inference(unit_resulting_resolution,[],[f20,f30]) ).
fof(f30,plain,
! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f124,plain,
( ~ sorti2(h(sK1))
| h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
| h(sK0) != op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f104,f87]) ).
fof(f104,plain,
( ~ sorti2(op2(h(sK0),h(sK0)))
| h(sK0) != op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0)))
| h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0))) ),
inference(resolution,[],[f38,f31]) ).
fof(f31,plain,
! [X0] :
( ~ sorti2(X0)
| op2(X0,op2(X0,X0)) = X0
| op2(op2(X0,X0),op2(X0,X0)) != X0
| ~ sorti2(op2(X0,X0)) ),
inference(equality_resolution,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| op2(X0,X0) != X1
| op2(X1,X1) != X0
| op2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| op2(X0,X0) != X1
| op2(X1,X1) != X0
| op2(X0,X1) = 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(f38,plain,
sorti2(h(sK0)),
inference(resolution,[],[f30,f21]) ).
fof(f74,plain,
op2(h(sK0),h(sK1)) = h(op1(sK0,sK1)),
inference(unit_resulting_resolution,[],[f21,f20,f29]) ).
fof(f122,plain,
op1(sK0,sK1) = j(h(op1(sK0,sK1))),
inference(forward_demodulation,[],[f121,f59]) ).
fof(f121,plain,
op1(j(h(sK0)),sK1) = j(h(op1(sK0,sK1))),
inference(forward_demodulation,[],[f120,f60]) ).
fof(f60,plain,
sK1 = j(h(sK1)),
inference(unit_resulting_resolution,[],[f20,f28]) ).
fof(f120,plain,
j(h(op1(sK0,sK1))) = op1(j(h(sK0)),j(h(sK1))),
inference(forward_demodulation,[],[f97,f74]) ).
fof(f97,plain,
op1(j(h(sK0)),j(h(sK1))) = j(op2(h(sK0),h(sK1))),
inference(unit_resulting_resolution,[],[f35,f38,f26]) ).
fof(f26,plain,
! [X6,X5] :
( ~ sorti2(X6)
| ~ sorti2(X5)
| j(op2(X5,X6)) = op1(j(X5),j(X6)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f86,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f85]) ).
fof(f85,plain,
( $false
| spl2_1 ),
inference(subsumption_resolution,[],[f84,f82]) ).
fof(f82,plain,
( op2(h(sK0),h(sK0)) != h(sK1)
| spl2_1 ),
inference(backward_demodulation,[],[f53,f80]) ).
fof(f53,plain,
( op2(op2(h(sK1),h(sK1)),op2(h(sK1),h(sK1))) != h(sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f84,plain,
op2(h(sK0),h(sK0)) = h(sK1),
inference(forward_demodulation,[],[f72,f17]) ).
fof(f17,plain,
op1(sK0,sK0) = sK1,
inference(cnf_transformation,[],[f15]) ).
fof(f72,plain,
op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
inference(unit_resulting_resolution,[],[f21,f21,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n025.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 15:02:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.48 % (6951)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.48 % (6958)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.18/0.49 % (6950)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.49 % (6943)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.49 % (6950)Instruction limit reached!
% 0.18/0.49 % (6950)------------------------------
% 0.18/0.49 % (6950)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49 % (6950)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49 % (6950)Termination reason: Unknown
% 0.18/0.49 % (6950)Termination phase: Saturation
% 0.18/0.49
% 0.18/0.49 % (6950)Memory used [KB]: 5884
% 0.18/0.49 % (6950)Time elapsed: 0.063 s
% 0.18/0.49 % (6950)Instructions burned: 3 (million)
% 0.18/0.49 % (6950)------------------------------
% 0.18/0.49 % (6950)------------------------------
% 0.18/0.49 % (6951)Instruction limit reached!
% 0.18/0.49 % (6951)------------------------------
% 0.18/0.49 % (6951)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49 % (6942)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.50 % (6949)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.50 % (6940)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.50 % (6959)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.18/0.50 % (6943)First to succeed.
% 0.18/0.50 % (6951)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50 % (6951)Termination reason: Unknown
% 0.18/0.50 % (6951)Termination phase: Saturation
% 0.18/0.50
% 0.18/0.50 % (6951)Memory used [KB]: 6012
% 0.18/0.50 % (6951)Time elapsed: 0.107 s
% 0.18/0.50 % (6951)Instructions burned: 7 (million)
% 0.18/0.50 % (6951)------------------------------
% 0.18/0.50 % (6951)------------------------------
% 0.18/0.51 % (6943)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (6943)------------------------------
% 0.18/0.51 % (6943)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (6943)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (6943)Termination reason: Refutation
% 0.18/0.51
% 0.18/0.51 % (6943)Memory used [KB]: 6012
% 0.18/0.51 % (6943)Time elapsed: 0.116 s
% 0.18/0.51 % (6943)Instructions burned: 5 (million)
% 0.18/0.51 % (6943)------------------------------
% 0.18/0.51 % (6943)------------------------------
% 0.18/0.51 % (6935)Success in time 0.166 s
%------------------------------------------------------------------------------