TSTP Solution File: ALG070+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ALG070+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 : n022.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 1.33s 0.53s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 12 unt; 0 def)
% Number of atoms : 203 ( 68 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 228 ( 79 ~; 65 |; 46 &)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 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 : 89 ( 81 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f234,plain,
$false,
inference(avatar_sat_refutation,[],[f197,f233]) ).
fof(f233,plain,
~ spl2_7,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f232,plain,
( $false
| ~ spl2_7 ),
inference(subsumption_resolution,[],[f231,f31]) ).
fof(f31,plain,
sK0 != op2(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( sK0 != op2(sK0,sK1)
& op2(sK0,sK0) = sK1
& sorti2(sK1)
& sorti2(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f18,f17]) ).
fof(f17,plain,
( ? [X0] :
( ? [X1] :
( op2(X0,X1) != X0
& op2(X0,X0) = X1
& sorti2(X1) )
& sorti2(X0) )
=> ( ? [X1] :
( op2(sK0,X1) != sK0
& op2(sK0,sK0) = X1
& sorti2(X1) )
& sorti2(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
( ? [X1] :
( op2(sK0,X1) != sK0
& op2(sK0,sK0) = X1
& sorti2(X1) )
=> ( sK0 != op2(sK0,sK1)
& op2(sK0,sK0) = sK1
& sorti2(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
? [X0] :
( ? [X1] :
( op2(X0,X1) != X0
& op2(X0,X0) = X1
& sorti2(X1) )
& sorti2(X0) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
? [X0] :
( ? [X1] :
( op2(X0,X0) = X1
& op2(X0,X1) != X0
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> ( op2(X0,X0) != X1
| op2(X0,X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f231,plain,
( sK0 = op2(sK0,sK1)
| ~ spl2_7 ),
inference(forward_demodulation,[],[f229,f36]) ).
fof(f36,plain,
h(j(sK0)) = sK0,
inference(resolution,[],[f24,f28]) ).
fof(f28,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f19]) ).
fof(f24,plain,
! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ! [X0] :
( ~ sorti2(X0)
| sorti1(j(X0)) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [X2] :
( ~ sorti2(X2)
| ! [X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
& ! [X4] :
( ~ sorti1(X4)
| sorti2(h(X4)) )
& ! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 )
& ! [X6] :
( ! [X7] :
( ~ sorti1(X7)
| op2(h(X6),h(X7)) = h(op1(X6,X7)) )
| ~ sorti1(X6) ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ! [X0] :
( ~ sorti2(X0)
| sorti1(j(X0)) )
& ! [X7] :
( h(j(X7)) = X7
| ~ sorti2(X7) )
& ! [X5] :
( ~ sorti2(X5)
| ! [X6] :
( ~ sorti2(X6)
| j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X1] :
( ~ sorti1(X1)
| sorti2(h(X1)) )
& ! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 )
& ! [X3] :
( ! [X4] :
( ~ sorti1(X4)
| h(op1(X3,X4)) = op2(h(X3),h(X4)) )
| ~ sorti1(X3) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
( ! [X7] :
( h(j(X7)) = X7
| ~ sorti2(X7) )
& ! [X3] :
( ! [X4] :
( ~ sorti1(X4)
| h(op1(X3,X4)) = op2(h(X3),h(X4)) )
| ~ sorti1(X3) )
& ! [X5] :
( ~ sorti2(X5)
| ! [X6] :
( ~ sorti2(X6)
| j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 )
& ! [X0] :
( ~ sorti2(X0)
| sorti1(j(X0)) )
& ! [X1] :
( ~ sorti1(X1)
| sorti2(h(X1)) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X0] :
( sorti2(X0)
=> sorti1(j(X0)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 ) ) ),
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 )
& ! [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)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 ) ) ),
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 )
& ! [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)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f229,plain,
( h(j(sK0)) = op2(sK0,sK1)
| ~ spl2_7 ),
inference(superposition,[],[f110,f225]) ).
fof(f225,plain,
( j(op2(sK0,sK1)) = j(sK0)
| ~ spl2_7 ),
inference(forward_demodulation,[],[f223,f204]) ).
fof(f204,plain,
( op1(j(sK0),j(sK1)) = j(sK0)
| ~ spl2_7 ),
inference(forward_demodulation,[],[f201,f183]) ).
fof(f183,plain,
j(sK1) = op1(j(sK0),j(sK0)),
inference(forward_demodulation,[],[f181,f30]) ).
fof(f30,plain,
op2(sK0,sK0) = sK1,
inference(cnf_transformation,[],[f19]) ).
fof(f181,plain,
op1(j(sK0),j(sK0)) = j(op2(sK0,sK0)),
inference(resolution,[],[f86,f28]) ).
fof(f86,plain,
! [X5] :
( ~ sorti2(X5)
| op1(j(X5),j(sK0)) = j(op2(X5,sK0)) ),
inference(resolution,[],[f23,f28]) ).
fof(f23,plain,
! [X2,X3] :
( ~ sorti2(X3)
| ~ sorti2(X2)
| j(op2(X2,X3)) = op1(j(X2),j(X3)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f201,plain,
( j(sK0) = op1(j(sK0),op1(j(sK0),j(sK0)))
| ~ spl2_7 ),
inference(resolution,[],[f188,f34]) ).
fof(f34,plain,
! [X0] :
( ~ sorti1(X0)
| op1(X0,op1(X0,X0)) = X0 ),
inference(subsumption_resolution,[],[f33,f32]) ).
fof(f32,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X0)
| ~ sorti1(X1) ),
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(f33,plain,
! [X0] :
( op1(X0,op1(X0,X0)) = X0
| ~ sorti1(X0)
| ~ sorti1(op1(X0,X0)) ),
inference(equality_resolution,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(X0,X0) != X1
| op1(X0,X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0] :
( ~ sorti1(X0)
| ! [X1] :
( ~ sorti1(X1)
| op1(X0,X0) != X1
| op1(X0,X1) = X0 ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
! [X0] :
( ! [X1] :
( op1(X0,X1) = X0
| op1(X0,X0) != X1
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> ( op1(X0,X1) = X0
| op1(X0,X0) != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f188,plain,
( sorti1(j(sK0))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f187,plain,
( spl2_7
<=> sorti1(j(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f223,plain,
j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)),
inference(resolution,[],[f87,f28]) ).
fof(f87,plain,
! [X6] :
( ~ sorti2(X6)
| j(op2(X6,sK1)) = op1(j(X6),j(sK1)) ),
inference(resolution,[],[f23,f29]) ).
fof(f29,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f110,plain,
op2(sK0,sK1) = h(j(op2(sK0,sK1))),
inference(resolution,[],[f66,f28]) ).
fof(f66,plain,
! [X6] :
( ~ sorti2(X6)
| h(j(op2(X6,sK1))) = op2(X6,sK1) ),
inference(resolution,[],[f41,f29]) ).
fof(f41,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X0,X1) = h(j(op2(X0,X1))) ),
inference(resolution,[],[f27,f24]) ).
fof(f27,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X0)
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
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(f197,plain,
spl2_7,
inference(avatar_contradiction_clause,[],[f196]) ).
fof(f196,plain,
( $false
| spl2_7 ),
inference(subsumption_resolution,[],[f195,f28]) ).
fof(f195,plain,
( ~ sorti2(sK0)
| spl2_7 ),
inference(resolution,[],[f189,f25]) ).
fof(f25,plain,
! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f189,plain,
( ~ sorti1(j(sK0))
| spl2_7 ),
inference(avatar_component_clause,[],[f187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 14:54:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.50 % (2763)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51 % (2768)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51 % (2776)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.52 % (2763)Instruction limit reached!
% 0.19/0.52 % (2763)------------------------------
% 0.19/0.52 % (2763)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (2763)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (2763)Termination reason: Unknown
% 0.19/0.52 % (2763)Termination phase: Saturation
% 0.19/0.52
% 0.19/0.52 % (2763)Memory used [KB]: 5500
% 0.19/0.52 % (2763)Time elapsed: 0.123 s
% 0.19/0.52 % (2763)Instructions burned: 9 (million)
% 0.19/0.52 % (2763)------------------------------
% 0.19/0.52 % (2763)------------------------------
% 0.19/0.52 % (2783)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.52 % (2756)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.52 % (2784)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.52 TRYING [1]
% 0.19/0.52 TRYING [2]
% 0.19/0.52 % (2764)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.52 % (2764)Instruction limit reached!
% 0.19/0.52 % (2764)------------------------------
% 0.19/0.52 % (2764)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (2764)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (2764)Termination reason: Unknown
% 0.19/0.52 % (2764)Termination phase: Preprocessing 3
% 0.19/0.52
% 0.19/0.52 % (2764)Memory used [KB]: 895
% 0.19/0.52 % (2764)Time elapsed: 0.002 s
% 0.19/0.52 % (2764)Instructions burned: 2 (million)
% 0.19/0.52 % (2764)------------------------------
% 0.19/0.52 % (2764)------------------------------
% 0.19/0.52 % (2760)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 TRYING [3]
% 0.19/0.52 % (2770)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)
% 0.19/0.53 TRYING [4]
% 0.19/0.53 % (2758)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.53 % (2761)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.53 % (2768)First to succeed.
% 0.19/0.53 % (2759)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.33/0.53 % (2768)Refutation found. Thanks to Tanya!
% 1.33/0.53 % SZS status Theorem for theBenchmark
% 1.33/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.33/0.53 % (2768)------------------------------
% 1.33/0.53 % (2768)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.53 % (2768)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.53 % (2768)Termination reason: Refutation
% 1.33/0.53
% 1.33/0.53 % (2768)Memory used [KB]: 5628
% 1.33/0.53 % (2768)Time elapsed: 0.131 s
% 1.33/0.53 % (2768)Instructions burned: 9 (million)
% 1.33/0.53 % (2768)------------------------------
% 1.33/0.53 % (2768)------------------------------
% 1.33/0.53 % (2755)Success in time 0.186 s
%------------------------------------------------------------------------------