%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n010.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 09:09:29 AM UTC 2026
% Result : Theorem 3.34s 0.93s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 16 unt; 3 def)
% Number of atoms : 184 ( 46 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 81 ~; 70 |; 32 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 65 !; 4 ?)
% 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,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,
( ! [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(f8,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,[],[f7]) ).
fof(f9,plain,
? [X0] :
( ? [X1] :
( op2(X0,X0) = X1
& op2(X0,X1) != X0
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( op2(X0,X0) = X1
& op2(X0,X1) != X0
& sorti2(X1) )
& sorti2(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ! [X1] :
( op1(X0,X0) != X1
| op1(X0,X1) = X0
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
! [X0] :
( ! [X1] :
( op1(X0,X0) != X1
| op1(X0,X1) = X0
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(flattening,[],[f11]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f15,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,[],[f8]) ).
fof(f16,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)],[f10]) ).
fof(f17,plain,
! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) ),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
sK0 != op2(sK0,sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
sK1 = op2(sK0,sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] :
( op1(X0,X0) != X1
| op1(X0,X1) = X0
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,definition,
~ sP2(sK0),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f31,plain,
sP2(op2(sK0,sK1)),
inference(inequality_splitting,[],[f25,f30]) ).
fof(f32,plain,
! [X0] :
( op1(X0,op1(X0,X0)) = X0
| ~ sorti1(op1(X0,X0))
| ~ sorti1(X0) ),
inference(equality_resolution,[],[f27]) ).
fof(f35,plain,
( j(sK1) = op1(j(sK0),j(sK0))
| ~ sorti2(sK0)
| ~ sorti2(sK0) ),
inference(superposition,[],[f21,f26]) ).
fof(f36,plain,
! [X0,X1] :
( op2(X0,X1) = h(op1(j(X0),j(X1)))
| ~ sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(superposition,[],[f20,f21]) ).
fof(f38,plain,
( j(sK1) = op1(j(sK0),j(sK0))
| ~ sorti2(sK0) ),
inference(duplicate_literal_removal,[],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( op2(X0,X1) = h(op1(j(X0),j(X1)))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(forward_subsumption_resolution,[],[f36,f29]) ).
fof(f41,plain,
j(sK1) = op1(j(sK0),j(sK0)),
inference(forward_subsumption_resolution,[],[f38,f23]) ).
fof(f53,plain,
( sorti1(op1(j(sK0),j(sK0)))
| ~ sorti2(sK1) ),
inference(superposition,[],[f17,f41]) ).
fof(f54,plain,
sorti1(op1(j(sK0),j(sK0))),
inference(forward_subsumption_resolution,[],[f53,f24]) ).
fof(f81,plain,
( sP2(h(op1(j(sK0),j(sK1))))
| ~ sorti2(sK1)
| ~ sorti2(sK0) ),
inference(superposition,[],[f31,f40]) ).
fof(f90,plain,
( sP2(h(op1(j(sK0),j(sK1))))
| ~ sorti2(sK0) ),
inference(forward_subsumption_resolution,[],[f81,f24]) ).
fof(f93,plain,
sP2(h(op1(j(sK0),j(sK1)))),
inference(forward_subsumption_resolution,[],[f90,f23]) ).
fof(f95,plain,
sP2(h(op1(j(sK0),op1(j(sK0),j(sK0))))),
inference(forward_demodulation,[],[f93,f41]) ).
fof(f156,plain,
( sP2(h(j(sK0)))
| ~ sorti1(op1(j(sK0),j(sK0)))
| ~ sorti1(j(sK0)) ),
inference(superposition,[],[f95,f32]) ).
fof(f157,plain,
( sP2(h(j(sK0)))
| ~ sorti1(j(sK0)) ),
inference(forward_subsumption_resolution,[],[f156,f54]) ).
fof(f159,definition,
( spl3_1
<=> sorti1(j(sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f161,plain,
( ~ sorti1(j(sK0))
| spl3_1 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f163,definition,
( spl3_2
<=> sP2(h(j(sK0))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f165,plain,
( sP2(h(j(sK0)))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f157,f163,f159]) ).
fof(f186,plain,
( ~ sorti2(sK0)
| spl3_1 ),
inference(resolution,[],[f161,f17]) ).
fof(f187,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f186,f23]) ).
fof(f188,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f211,plain,
( sP2(sK0)
| ~ sorti2(sK0)
| ~ spl3_2 ),
inference(superposition,[],[f165,f20]) ).
fof(f212,plain,
( ~ sorti2(sK0)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f211,f30]) ).
fof(f213,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f212,f23]) ).
fof(f214,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f213]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f166]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f188]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f214]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f215,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG070+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n010.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
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 19:25:17 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/0.93 % (2236026)Detected formulas, will run a generic FOF schedule.
% 3.34/0.93 % (2236033)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3154517828:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/0.93 % (2236031)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2107733305:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/0.93 % (2236035)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3968136748:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/0.93 % (2236036)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3025697955:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/0.93 % (2236034)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=171952715:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/0.93 % (2236037)dis-21_1_sil=8000:lcm=predicate:random_seed=947655274:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.34/0.93 % (2236032)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=528178883:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/0.93 % (2236037)Refutation not found, incomplete strategy
% 3.34/0.93 % (2236037)------------------------------
% 3.34/0.93 % (2236037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/0.93 % (2236037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.93 % (2236037)CaDiCaL version: 2.1.3
% 3.34/0.93 % (2236037)Termination reason: Refutation not found, incomplete strategy
% 3.34/0.93 % (2236037)Time elapsed: 0.002 s
% 3.34/0.93 % (2236037)Peak memory usage: 88 MB
% 3.34/0.93 % (2236037)Instructions burned: 1 (million)
% 3.34/0.93 % (2236034)First to succeed.
% 3.34/0.93 % (2236034)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2236026"
% 3.34/0.93 % (2236035)Also succeeded, but the first one will report.
% 3.34/0.93 % (2236036)Also succeeded, but the first one will report.
% 3.34/0.93 % (2236037)------------------------------
% 3.34/0.93 % (2236037)------------------------------
% 3.34/0.93 % (2236034)Refutation found. Thanks to Tanya!
% 3.34/0.93 % SZS status Theorem for theBenchmark
% 3.34/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/0.93 % (2236034)------------------------------
% 3.34/0.93 % (2236034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/0.93 % (2236034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.93 % (2236034)CaDiCaL version: 2.1.3
% 3.34/0.93 % (2236034)Termination reason: Refutation
% 3.34/0.93 % (2236034)Time elapsed: 0.007 s
% 3.34/0.93 % (2236034)Peak memory usage: 89 MB
% 3.34/0.93 % (2236034)Instructions burned: 8 (million)
% 3.34/0.93 % (2236034)------------------------------
% 3.34/0.93 % (2236034)------------------------------
% 3.34/0.93 % (2236026)Success in time 0.43 s
% 3.34/0.93 % Vampire exiting
%------------------------------------------------------------------------------