%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG029+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:20:09 AM UTC 2026
% Result : Theorem 0.25s 0.33s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 13 unt; 1 def)
% Number of atoms : 155 ( 45 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 170 ( 63 ~; 55 |; 27 &)
% ( 1 <=>; 24 =>; 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 : 69 ( 0 sgn 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,X1) = op1(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,X1) = op2(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,conjecture,
( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [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 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f6,negated_conjecture,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [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 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f8,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( op1(X0,X1) = op1(X1,X0)
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( op2(X0,X1) != op2(X1,X0)
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
( op2(sK0,sK1) != op2(sK1,sK0)
& sorti2(sK1)
& sorti2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
fof(f14,plain,
( ! [X0] :
( ! [X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) )
& ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) )
& ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ) ),
inference(rectify,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f17,plain,
! [X0,X1] :
( ~ sorti1(X1)
| op1(X0,X1) = op1(X1,X0)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
op2(sK0,sK1) != op2(sK1,sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK0)) = op1(j(X0),j(sK0)) ),
inference(resolution,[],[f18,f25]) ).
fof(f38,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK1)) = op1(j(X0),j(sK1)) ),
inference(resolution,[],[f19,f25]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X0) = h(j(op2(X1,X0))) ),
inference(resolution,[],[f16,f24]) ).
fof(f55,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti1(X0)
| op1(X0,j(X1)) = op1(j(X1),X0) ),
inference(resolution,[],[f17,f21]) ).
fof(f60,plain,
j(op2(sK1,sK0)) = op1(j(sK1),j(sK0)),
inference(resolution,[],[f34,f19]) ).
fof(f63,plain,
j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)),
inference(resolution,[],[f38,f18]) ).
fof(f83,plain,
! [X0] :
( ~ sorti2(X0)
| op2(sK0,X0) = h(j(op2(sK0,X0))) ),
inference(resolution,[],[f48,f18]) ).
fof(f84,plain,
! [X0] :
( ~ sorti2(X0)
| op2(sK1,X0) = h(j(op2(sK1,X0))) ),
inference(resolution,[],[f48,f19]) ).
fof(f96,plain,
! [X0] :
( ~ sorti1(X0)
| op1(j(sK0),X0) = op1(X0,j(sK0)) ),
inference(resolution,[],[f55,f18]) ).
fof(f111,definition,
( spl2_3
<=> sorti1(j(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f112,plain,
( sorti1(j(sK1))
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( ~ sorti1(j(sK1))
| spl2_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f125,plain,
( ~ sorti2(sK1)
| spl2_3 ),
inference(resolution,[],[f113,f21]) ).
fof(f126,plain,
( $false
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f125,f19]) ).
fof(f127,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f178,plain,
op2(sK0,sK1) = h(j(op2(sK0,sK1))),
inference(resolution,[],[f83,f19]) ).
fof(f189,plain,
op2(sK1,sK0) = h(j(op2(sK1,sK0))),
inference(resolution,[],[f84,f18]) ).
fof(f199,plain,
( op1(j(sK1),j(sK0)) = op1(j(sK0),j(sK1))
| ~ spl2_3 ),
inference(resolution,[],[f96,f112]) ).
fof(f201,plain,
( op1(j(sK1),j(sK0)) = j(op2(sK0,sK1))
| ~ spl2_3 ),
inference(forward_demodulation,[],[f199,f63]) ).
fof(f375,plain,
( j(op2(sK1,sK0)) = j(op2(sK0,sK1))
| ~ spl2_3 ),
inference(superposition,[],[f201,f60]) ).
fof(f386,plain,
( op2(sK1,sK0) = h(j(op2(sK0,sK1)))
| ~ spl2_3 ),
inference(superposition,[],[f189,f375]) ).
fof(f389,plain,
( op2(sK0,sK1) = op2(sK1,sK0)
| ~ spl2_3 ),
inference(forward_demodulation,[],[f386,f178]) ).
fof(f390,plain,
( $false
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f389,f20]) ).
fof(f391,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f390]) ).
cnf(s4,plain,
spl2_3,
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
~ spl2_3,
inference(sat_conversion,[],[f391]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s4,s5]) ).
fof(f392,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG029+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 19:19:30 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.33 % (3685374)Will run a generic schedule for satisfiability detection.
% 0.25/0.33 % (3685381)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3183338150:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.33 % (3685380)% WARNING: option uhcvi not known.
% 0.25/0.33 % (3685379)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1815715388_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.33 % (3685380)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1614681602:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.33 % (3685382)dis+10_1_sil=32000:sp=arity:random_seed=525539013:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.33 % (3685383)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1881706519:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.33 % (3685384)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1671528303:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.33 % (3685385)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4045126154:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.33 % TRYING [1]
% 0.25/0.33 % TRYING [2]
% 0.25/0.33 % TRYING [3]
% 0.25/0.33 % (3685382) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3685374-3685382"...
% 0.25/0.33 % TRYING [4]
% 0.25/0.33 % (3685384) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3685374-3685384"...
% 0.25/0.33 % (3685382)...printing done.
% 0.25/0.33 % (3685384)...printing done.
% 0.25/0.33 % (3685382)Refutation found. Thanks to Tanya!
% 0.25/0.33 % SZS status Theorem for theBenchmark
% 0.25/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.33 % (3685382)------------------------------
% 0.25/0.33 % (3685382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.33 % (3685382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.33 % (3685382)CaDiCaL version: 2.1.3
% 0.25/0.33 % (3685382)Termination reason: Refutation
% 0.25/0.33 % (3685382)Time elapsed: 0.017 s
% 0.25/0.33 % (3685382)Peak memory usage: 12 MB
% 0.25/0.33 % (3685382)Instructions burned: 16 (million)
% 0.25/0.33 % (3685374)Success in time 0.054 s
% 0.25/0.33 % Vampire exiting
%------------------------------------------------------------------------------