TSTP Solution File: ALG029+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG029+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.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 : Mon May 20 18:22:57 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 159 ( 54 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 177 ( 59 ~; 46 |; 37 &)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f330,plain,
$false,
inference(subsumption_resolution,[],[f329,f26]) ).
fof(f26,plain,
op2(sK0,sK1) != op2(sK1,sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( op2(sK0,sK1) != op2(sK1,sK0)
& sorti2(sK1)
& sorti2(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f16,f15]) ).
fof(f15,plain,
( ? [X0] :
( ? [X1] :
( op2(X0,X1) != op2(X1,X0)
& sorti2(X1) )
& sorti2(X0) )
=> ( ? [X1] :
( op2(sK0,X1) != op2(X1,sK0)
& sorti2(X1) )
& sorti2(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ? [X1] :
( op2(sK0,X1) != op2(X1,sK0)
& sorti2(X1) )
=> ( op2(sK0,sK1) != op2(sK1,sK0)
& sorti2(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( op2(X0,X1) != op2(X1,X0)
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,X1) = op2(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f329,plain,
op2(sK0,sK1) = op2(sK1,sK0),
inference(forward_demodulation,[],[f327,f63]) ).
fof(f63,plain,
op2(sK0,sK1) = h(j(op2(sK0,sK1))),
inference(resolution,[],[f58,f25]) ).
fof(f25,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f58,plain,
! [X0] :
( ~ sorti2(X0)
| op2(sK0,X0) = h(j(op2(sK0,X0))) ),
inference(resolution,[],[f43,f24]) ).
fof(f24,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f43,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X0) = h(j(op2(X1,X0))) ),
inference(resolution,[],[f29,f22]) ).
fof(f22,plain,
! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
( ! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( ! [X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5) )
| ~ sorti1(X4) )
& ! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) )
& ! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X0] :
( sorti2(X0)
=> sorti1(j(X0)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X3] :
( sorti2(X3)
=> h(j(X3)) = X3 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti1(X6)
=> ! [X7] :
( sorti1(X7)
=> h(op1(X6,X7)) = op2(h(X6),h(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 )
& ! [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)) ) ) ) ),
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 )
& ! [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)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f29,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f327,plain,
op2(sK1,sK0) = h(j(op2(sK0,sK1))),
inference(superposition,[],[f136,f309]) ).
fof(f309,plain,
j(op2(sK0,sK1)) = j(op2(sK1,sK0)),
inference(superposition,[],[f308,f217]) ).
fof(f217,plain,
j(op2(sK1,sK0)) = op1(j(sK1),j(sK0)),
inference(resolution,[],[f91,f25]) ).
fof(f91,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK0)) = op1(j(X0),j(sK0)) ),
inference(resolution,[],[f21,f24]) ).
fof(f21,plain,
! [X2,X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f308,plain,
j(op2(sK0,sK1)) = op1(j(sK1),j(sK0)),
inference(forward_demodulation,[],[f307,f227]) ).
fof(f227,plain,
j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)),
inference(resolution,[],[f92,f24]) ).
fof(f92,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK1)) = op1(j(X0),j(sK1)) ),
inference(resolution,[],[f21,f25]) ).
fof(f307,plain,
op1(j(sK1),j(sK0)) = op1(j(sK0),j(sK1)),
inference(resolution,[],[f240,f25]) ).
fof(f240,plain,
! [X0] :
( ~ sorti2(X0)
| op1(j(X0),j(sK0)) = op1(j(sK0),j(X0)) ),
inference(resolution,[],[f238,f19]) ).
fof(f19,plain,
! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) ),
inference(cnf_transformation,[],[f14]) ).
fof(f238,plain,
! [X0] :
( ~ sorti1(X0)
| op1(X0,j(sK0)) = op1(j(sK0),X0) ),
inference(resolution,[],[f153,f24]) ).
fof(f153,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti1(X0)
| op1(X0,j(X1)) = op1(j(X1),X0) ),
inference(resolution,[],[f28,f19]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sorti1(X1)
| op1(X0,X1) = op1(X1,X0)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( ! [X1] :
( op1(X0,X1) = op1(X1,X0)
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,X1) = op1(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f136,plain,
op2(sK1,sK0) = h(j(op2(sK1,sK0))),
inference(resolution,[],[f59,f24]) ).
fof(f59,plain,
! [X0] :
( ~ sorti2(X0)
| op2(sK1,X0) = h(j(op2(sK1,X0))) ),
inference(resolution,[],[f43,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG029+1 : TPTP v8.2.0. Released v2.7.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 23:41:52 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (9515)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (9518)WARNING: value z3 for option sas not known
% 0.14/0.37 % (9518)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)
% 0.14/0.37 % (9517)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (9516)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (9519)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (9520)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)
% 0.14/0.37 % (9521)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)
% 0.14/0.37 % (9522)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 [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (9518)First to succeed.
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 % (9518)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9515"
% 0.14/0.38 % (9518)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (9518)------------------------------
% 0.14/0.38 % (9518)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (9518)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (9518)Memory used [KB]: 900
% 0.14/0.38 % (9518)Time elapsed: 0.012 s
% 0.14/0.38 % (9518)Instructions burned: 18 (million)
% 0.14/0.38 % (9515)Success in time 0.025 s
%------------------------------------------------------------------------------