%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG070+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 : n013.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 09:21:14 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 16 unt; 3 def)
% Number of atoms : 195 ( 56 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 216 ( 82 ~; 73 |; 32 &)
% ( 3 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 72 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
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,X0) != X1
| op1(X0,X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> ( op2(X0,X0) != X1
| op2(X0,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(f7,plain,
! [X0] :
( ! [X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f8,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( op1(X0,X0) != X1
| op1(X0,X1) = X0
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
! [X0] :
( ! [X1] :
( op1(X0,X0) != X1
| op1(X0,X1) = X0
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
? [X0] :
( ? [X1] :
( op2(X0,X0) = X1
& op2(X0,X1) != X0
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f12,plain,
? [X0] :
( ? [X1] :
( op2(X0,X0) = X1
& op2(X0,X1) != X0
& sorti2(X1) )
& sorti2(X0) ),
inference(flattening,[],[f11]) ).
fof(f13,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(f14,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,[],[f13]) ).
fof(f15,plain,
( sK1 = op2(sK0,sK0)
& sK0 != op2(sK0,sK1)
& sorti2(sK1)
& sorti2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f16,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,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f19,plain,
! [X0,X1] :
( op1(X0,X0) != X1
| op1(X0,X1) = X0
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
sK0 != op2(sK0,sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
sK1 = op2(sK0,sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0] :
( ~ sorti1(op1(X0,X0))
| op1(X0,op1(X0,X0)) = X0
| ~ sorti1(X0) ),
inference(equality_resolution,[],[f19]) ).
fof(f38,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK0)) = op1(j(X0),j(sK0)) ),
inference(resolution,[],[f20,f28]) ).
fof(f40,plain,
sK0 = h(j(sK0)),
inference(resolution,[],[f20,f27]) ).
fof(f42,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK1)) = op1(j(X0),j(sK1)) ),
inference(resolution,[],[f21,f28]) ).
fof(f58,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X0) = h(j(op2(X1,X0))) ),
inference(resolution,[],[f18,f27]) ).
fof(f63,plain,
j(op2(sK0,sK0)) = op1(j(sK0),j(sK0)),
inference(resolution,[],[f38,f20]) ).
fof(f65,plain,
j(sK1) = op1(j(sK0),j(sK0)),
inference(forward_demodulation,[],[f63,f23]) ).
fof(f68,plain,
( sorti1(j(sK1))
| ~ sorti1(j(sK0))
| ~ sorti1(j(sK0)) ),
inference(superposition,[],[f17,f65]) ).
fof(f69,plain,
( ~ sorti1(j(sK1))
| j(sK0) = op1(j(sK0),j(sK1))
| ~ sorti1(j(sK0)) ),
inference(superposition,[],[f30,f65]) ).
fof(f70,plain,
( sorti1(j(sK1))
| ~ sorti1(j(sK0)) ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f72,definition,
( spl2_1
<=> sorti1(j(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f74,plain,
( ~ sorti1(j(sK0))
| spl2_1 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl2_2
<=> j(sK0) = op1(j(sK0),j(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f78,plain,
( j(sK0) = op1(j(sK0),j(sK1))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl2_3
<=> sorti1(j(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f83,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f69,f80,f76,f72]) ).
fof(f84,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f70,f80,f72]) ).
fof(f87,plain,
op1(j(sK0),j(sK1)) = j(op2(sK0,sK1)),
inference(resolution,[],[f42,f20]) ).
fof(f89,plain,
( ~ sorti2(sK0)
| spl2_1 ),
inference(resolution,[],[f74,f24]) ).
fof(f90,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f89,f20]) ).
fof(f91,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f104,plain,
! [X0] :
( ~ sorti2(X0)
| op2(sK0,X0) = h(j(op2(sK0,X0))) ),
inference(resolution,[],[f58,f20]) ).
fof(f144,plain,
( j(sK0) = j(op2(sK0,sK1))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f87,f78]) ).
fof(f177,plain,
op2(sK0,sK1) = h(j(op2(sK0,sK1))),
inference(resolution,[],[f104,f21]) ).
fof(f178,plain,
( op2(sK0,sK1) = h(j(sK0))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f177,f144]) ).
fof(f180,plain,
( sK0 = op2(sK0,sK1)
| ~ spl2_2 ),
inference(forward_demodulation,[],[f178,f40]) ).
fof(f181,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f180,f22]) ).
fof(f182,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f181]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f83]) ).
cnf(s2,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
spl2_1,
inference(sat_conversion,[],[f91]) ).
cnf(s6,plain,
~ spl2_2,
inference(sat_conversion,[],[f182]) ).
cnf(s7,plain,
spl2_3,
inference(rat,[],[s2,s3]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s7,s6,s3]) ).
fof(f183,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG070+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 19:24:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.28 % (1474996)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1475001)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=524185316_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % TRYING [1]
% 0.20/0.28 % TRYING [2]
% 0.20/0.28 % TRYING [3]
% 0.20/0.28 % TRYING [4]
% 0.20/0.28 % (1475002)% WARNING: option uhcvi not known.
% 0.20/0.28 % TRYING [5]
% 0.20/0.28 % (1475004)dis+10_1_sil=32000:sp=arity:random_seed=1075134083:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1475002)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3557337428:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (1475003)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3818889310:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (1475006)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2088713268:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (1475005)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3128963273:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (1475007)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1142799281:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % TRYING [6]
% 0.20/0.28 % (1475004) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1474996-1475004"...
% 0.20/0.28 % (1475004)...printing done.
% 0.20/0.28 % (1475004)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1475004)------------------------------
% 0.20/0.28 % (1475004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1475004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1475004)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1475004)Termination reason: Refutation
% 0.20/0.28 % (1475004)Time elapsed: 0.006 s
% 0.20/0.28 % (1475004)Peak memory usage: 12 MB
% 0.20/0.28 % (1475004)Instructions burned: 8 (million)
% 0.20/0.28 % (1474996)Success in time 0.049 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------