%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:18:06 AM UTC 2026
% Result : Theorem 2.15s 0.69s
% Output : Refutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 16 unt; 6 def)
% Number of atoms : 211 ( 31 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 239 ( 96 ~; 87 |; 27 &)
% ( 5 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 66 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,op1(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,op2(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/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/sandbox/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,op2(X0,X1)) != X1
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
! [X0] :
( ! [X1] :
( op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f13,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(f14,plain,
( sK1 != op2(sK0,op2(sK0,sK1))
& sorti2(sK1)
& sorti2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f15,plain,
! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
sK1 != op2(sK0,op2(sK0,sK1)),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,definition,
~ sP2(sK1),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f28,plain,
sP2(op2(sK0,op2(sK0,sK1))),
inference(inequality_splitting,[],[f23,f27]) ).
fof(f31,plain,
! [X0,X1] :
( op2(X0,X1) = h(op1(j(X0),j(X1)))
| ~ sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(superposition,[],[f18,f19]) ).
fof(f34,plain,
! [X0,X1] :
( op2(X0,X1) = h(op1(j(X0),j(X1)))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(forward_subsumption_resolution,[],[f31,f26]) ).
fof(f61,plain,
( sP2(h(op1(j(sK0),j(op2(sK0,sK1)))))
| ~ sorti2(op2(sK0,sK1))
| ~ sorti2(sK0) ),
inference(superposition,[],[f28,f34]) ).
fof(f63,plain,
! [X0,X1] :
( sorti2(h(op1(j(X0),j(X1))))
| ~ sorti2(X1)
| ~ sorti2(X0)
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(superposition,[],[f26,f34]) ).
fof(f65,plain,
! [X0,X1] :
( sorti2(h(op1(j(X0),j(X1))))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(duplicate_literal_removal,[],[f63]) ).
fof(f68,plain,
( sP2(h(op1(j(sK0),j(op2(sK0,sK1)))))
| ~ sorti2(op2(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f61,f21]) ).
fof(f73,definition,
( spl3_1
<=> sorti2(op2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f75,plain,
( ~ sorti2(op2(sK0,sK1))
| spl3_1 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl3_2
<=> sP2(h(op1(j(sK0),j(op2(sK0,sK1))))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f79,plain,
( sP2(h(op1(j(sK0),j(op2(sK0,sK1)))))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f68,f77,f73]) ).
fof(f84,plain,
( ~ sorti2(h(op1(j(sK0),j(sK1))))
| ~ sorti2(sK1)
| ~ sorti2(sK0)
| spl3_1 ),
inference(superposition,[],[f75,f34]) ).
fof(f85,plain,
( ~ sorti2(sK1)
| ~ sorti2(sK0)
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f84,f65]) ).
fof(f87,plain,
( ~ sorti2(sK0)
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f85,f22]) ).
fof(f90,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f87,f21]) ).
fof(f91,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f157,plain,
( sP2(h(op1(j(sK0),op1(j(sK0),j(sK1)))))
| ~ sorti2(sK1)
| ~ sorti2(sK0)
| ~ spl3_2 ),
inference(superposition,[],[f79,f19]) ).
fof(f158,plain,
( sP2(h(op1(j(sK0),op1(j(sK0),j(sK1)))))
| ~ sorti2(sK0)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f157,f22]) ).
fof(f160,plain,
( sP2(h(op1(j(sK0),op1(j(sK0),j(sK1)))))
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f158,f21]) ).
fof(f219,plain,
( sP2(h(j(sK1)))
| ~ sorti1(j(sK1))
| ~ sorti1(j(sK0))
| ~ spl3_2 ),
inference(superposition,[],[f160,f24]) ).
fof(f221,definition,
( spl3_5
<=> sorti1(j(sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f223,plain,
( ~ sorti1(j(sK0))
| spl3_5 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f225,definition,
( spl3_6
<=> sorti1(j(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f227,plain,
( ~ sorti1(j(sK1))
| spl3_6 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f229,definition,
( spl3_7
<=> sP2(h(j(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f231,plain,
( sP2(h(j(sK1)))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f232,plain,
( ~ spl3_5
| ~ spl3_6
| spl3_7
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f219,f77,f229,f225,f221]) ).
fof(f246,plain,
( ~ sorti2(sK0)
| spl3_5 ),
inference(resolution,[],[f223,f15]) ).
fof(f247,plain,
( $false
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f246,f21]) ).
fof(f248,plain,
spl3_5,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f302,plain,
( ~ sorti2(sK1)
| spl3_6 ),
inference(resolution,[],[f227,f15]) ).
fof(f303,plain,
( $false
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f302,f22]) ).
fof(f304,plain,
spl3_6,
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f401,plain,
( sP2(sK1)
| ~ sorti2(sK1)
| ~ spl3_7 ),
inference(superposition,[],[f231,f18]) ).
fof(f402,plain,
( ~ sorti2(sK1)
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f401,f27]) ).
fof(f403,plain,
( $false
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f402,f22]) ).
fof(f404,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f403]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
spl3_1,
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_5
| ~ spl3_6
| spl3_7 ),
inference(sat_conversion,[],[f232]) ).
cnf(s6,plain,
spl3_5,
inference(sat_conversion,[],[f248]) ).
cnf(s7,plain,
spl3_6,
inference(sat_conversion,[],[f304]) ).
cnf(s8,plain,
~ spl3_7,
inference(sat_conversion,[],[f404]) ).
cnf(s9,plain,
~ spl3_2,
inference(rat,[],[s5,s8,s7,s6]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s3]) ).
fof(f405,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 19:39:34 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running first-order theorem proving
% 0.09/0.12 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.15/0.69 % (3666774)Detected formulas, will run a generic FOF schedule.
% 2.15/0.69 % (3666779)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=2963280610:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.15/0.69 % (3666783)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3500325874:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.15/0.69 % (3666784)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1438366669:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.15/0.69 % (3666785)dis-21_1_sil=8000:lcm=predicate:random_seed=279028253: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)
% 2.15/0.69 % (3666782)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2221181764:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.15/0.69 % (3666780)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=2613872927:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.15/0.69 % (3666781)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=73470930:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.15/0.69 % (3666785)Refutation not found, incomplete strategy
% 2.15/0.69 % (3666785)------------------------------
% 2.15/0.69 % (3666785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/0.69 % (3666785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (3666785)CaDiCaL version: 2.1.3
% 2.15/0.69 % (3666785)Termination reason: Refutation not found, incomplete strategy
% 2.15/0.69 % (3666785)Time elapsed: 0.001 s
% 2.15/0.69 % (3666785)Peak memory usage: 88 MB
% 2.15/0.69 % (3666782)First to succeed.
% 2.15/0.69 % (3666782)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3666774"
% 2.15/0.69 % (3666784)Also succeeded, but the first one will report.
% 2.15/0.69 % (3666783)Also succeeded, but the first one will report.
% 2.15/0.69 % (3666785)------------------------------
% 2.15/0.69 % (3666785)------------------------------
% 2.15/0.69 % (3666782)Refutation found. Thanks to Tanya!
% 2.15/0.69 % SZS status Theorem for theBenchmark
% 2.15/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.15/0.69 % (3666782)------------------------------
% 2.15/0.69 % (3666782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.15/0.69 % (3666782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (3666782)CaDiCaL version: 2.1.3
% 2.15/0.69 % (3666782)Termination reason: Refutation
% 2.15/0.69 % (3666782)Time elapsed: 0.006 s
% 2.15/0.69 % (3666782)Peak memory usage: 89 MB
% 2.15/0.69 % (3666782)Instructions burned: 14 (million)
% 2.15/0.69 % (3666782)------------------------------
% 2.15/0.69 % (3666782)------------------------------
% 2.15/0.69 % (3666774)Success in time 0.279 s
% 2.15/0.69 % Vampire exiting
%------------------------------------------------------------------------------