%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 09:40:06 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 89 ( 18 unt; 6 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 215 ( 101 ~; 93 |; 8 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 71 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption) ).
fof(f2,axiom,
! [X0] :
( ( reflexive_rewrite(b,X0)
& reflexive_rewrite(c,X0) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_ax) ).
fof(f3,axiom,
! [X0] : equalish(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f4,axiom,
! [X0,X1] :
( equalish(X0,X1)
=> equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmtery) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( equalish(X0,X1)
& reflexive_rewrite(X1,X2) )
=> reflexive_rewrite(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution) ).
fof(f6,axiom,
! [X0,X1] :
( equalish(X0,X1)
=> reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).
fof(f7,axiom,
! [X0,X1] :
( rewrite(X0,X1)
=> reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(f8,axiom,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
=> ( equalish(X0,X1)
| rewrite(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equalish_or_rewrite) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( rewrite(X0,X1)
& rewrite(X0,X2) )
=> ? [X3] :
( rewrite(X1,X3)
& rewrite(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_diamond) ).
fof(f10,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f11,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
~ goal,
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] :
( reflexive_rewrite(X0,X2)
| ~ equalish(X0,X1)
| ~ reflexive_rewrite(X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f17,plain,
! [X0,X1,X2] :
( reflexive_rewrite(X0,X2)
| ~ equalish(X0,X1)
| ~ reflexive_rewrite(X1,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| ~ equalish(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| ~ rewrite(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( equalish(X0,X1)
| rewrite(X0,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0,X1] :
( equalish(X0,X1)
| rewrite(X0,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3] :
( rewrite(X1,X3)
& rewrite(X2,X3) )
| ~ rewrite(X0,X1)
| ~ rewrite(X0,X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X3] :
( rewrite(X1,X3)
& rewrite(X2,X3) )
| ~ rewrite(X0,X1)
| ~ rewrite(X0,X2) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( rewrite(X1,sK0(X1,X2))
& rewrite(X2,sK0(X1,X2)) )
| ~ rewrite(X0,X1)
| ~ rewrite(X0,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X1,X2))],[f23]) ).
fof(f25,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0] : equalish(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ equalish(X0,X1)
| reflexive_rewrite(X0,X2)
| ~ reflexive_rewrite(X1,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( ~ rewrite(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1] :
( ~ reflexive_rewrite(X0,X1)
| rewrite(X0,X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| rewrite(X2,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| rewrite(X1,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
~ goal,
inference(cnf_transformation,[],[f12]) ).
fof(f38,definition,
( spl1_1
<=> ! [X0] :
( ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] :
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl1_2
<=> goal ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f44,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f27,f41,f38]) ).
fof(f45,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f36,f41]) ).
fof(f47,plain,
! [X0] : reflexive_rewrite(X0,X0),
inference(resolution,[],[f31,f28]) ).
fof(f48,plain,
( ~ reflexive_rewrite(b,c)
| ~ spl1_1 ),
inference(resolution,[],[f39,f47]) ).
fof(f50,plain,
( rewrite(a,c)
| equalish(a,c) ),
inference(resolution,[],[f33,f25]) ).
fof(f51,plain,
( rewrite(a,b)
| equalish(a,b) ),
inference(resolution,[],[f33,f26]) ).
fof(f54,definition,
( spl1_3
<=> equalish(a,b) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f56,plain,
( equalish(a,b)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f58,definition,
( spl1_4
<=> rewrite(a,b) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f60,plain,
( rewrite(a,b)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f51,f58,f54]) ).
fof(f63,definition,
( spl1_5
<=> equalish(a,c) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f65,plain,
( equalish(a,c)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl1_6
<=> rewrite(a,c) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f69,plain,
( rewrite(a,c)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl1_5
| spl1_6 ),
inference(avatar_split_clause,[],[f50,f67,f63]) ).
fof(f71,plain,
( ! [X0] :
( rewrite(b,sK0(X0,b))
| ~ rewrite(a,X0) )
| ~ spl1_4 ),
inference(resolution,[],[f60,f34]) ).
fof(f73,plain,
( ! [X0] :
( rewrite(X0,sK0(X0,b))
| ~ rewrite(a,X0) )
| ~ spl1_4 ),
inference(resolution,[],[f35,f60]) ).
fof(f76,plain,
( equalish(c,a)
| ~ spl1_5 ),
inference(resolution,[],[f65,f29]) ).
fof(f77,plain,
( ! [X0] :
( ~ reflexive_rewrite(a,X0)
| reflexive_rewrite(c,X0) )
| ~ spl1_5 ),
inference(resolution,[],[f76,f30]) ).
fof(f86,plain,
( ! [X0] :
( reflexive_rewrite(b,sK0(X0,b))
| ~ rewrite(a,X0) )
| ~ spl1_4 ),
inference(resolution,[],[f71,f32]) ).
fof(f88,plain,
( reflexive_rewrite(c,b)
| ~ spl1_5 ),
inference(resolution,[],[f77,f26]) ).
fof(f92,plain,
( ! [X0] :
( reflexive_rewrite(X0,sK0(X0,b))
| ~ rewrite(a,X0) )
| ~ spl1_4 ),
inference(resolution,[],[f73,f32]) ).
fof(f94,plain,
( ~ reflexive_rewrite(b,b)
| ~ spl1_1
| ~ spl1_5 ),
inference(resolution,[],[f88,f39]) ).
fof(f105,plain,
( $false
| ~ spl1_1
| ~ spl1_5 ),
inference(forward_subsumption_resolution,[],[f94,f47]) ).
fof(f106,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f118,plain,
( ~ rewrite(a,c)
| ~ reflexive_rewrite(b,sK0(c,b))
| ~ spl1_1
| ~ spl1_4 ),
inference(resolution,[],[f92,f39]) ).
fof(f119,plain,
( ~ reflexive_rewrite(b,sK0(c,b))
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f118,f69]) ).
fof(f123,plain,
( ~ rewrite(a,c)
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(resolution,[],[f119,f86]) ).
fof(f124,plain,
( $false
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f123,f69]) ).
fof(f125,plain,
( ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f124]) ).
fof(f128,plain,
( equalish(b,a)
| ~ spl1_3 ),
inference(resolution,[],[f56,f29]) ).
fof(f129,plain,
( ! [X0] :
( ~ reflexive_rewrite(a,X0)
| reflexive_rewrite(b,X0) )
| ~ spl1_3 ),
inference(resolution,[],[f128,f30]) ).
fof(f136,plain,
( reflexive_rewrite(b,c)
| ~ spl1_3 ),
inference(resolution,[],[f129,f25]) ).
fof(f149,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f136,f48]) ).
fof(f150,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f149]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
( spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f70]) ).
cnf(s6,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f106]) ).
cnf(s7,plain,
( ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s9,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f150]) ).
cnf(s10,plain,
spl1_1,
inference(rat,[],[s1,s2]) ).
cnf(s11,plain,
~ spl1_3,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
~ spl1_5,
inference(rat,[],[s6,s10]) ).
cnf(s13,plain,
spl1_4,
inference(rat,[],[s3,s11]) ).
cnf(s14,plain,
spl1_6,
inference(rat,[],[s4,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s7,s10,s14,s13]) ).
fof(f151,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:44:50 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.28 % (604964)Will run a generic schedule for satisfiability detection.
% 0.08/0.28 % (604973)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1721021354:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.28 % (604970)% WARNING: option uhcvi not known.
% 0.08/0.28 % (604972)dis+10_1_sil=32000:sp=arity:random_seed=4257627935:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.28 % (604969)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=778003302_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.28 % (604970)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2839501302:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.28 % (604971)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3633796148:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.28 % (604974)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2127579713:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.28 % (604975)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1608768210:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.28 % TRYING [1]
% 0.08/0.28 % TRYING [2]
% 0.08/0.28 % TRYING [3]
% 0.08/0.28 % TRYING [4]
% 0.08/0.28 % (604972) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-604964-604972"...
% 0.08/0.28 % (604974) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-604964-604974"...
% 0.08/0.28 % TRYING [5]
% 0.08/0.28 % TRYING [6]
% 0.08/0.28 % (604972)...printing done.
% 0.08/0.28 % (604974)...printing done.
% 0.08/0.28 % TRYING [7]
% 0.08/0.28 % (604972)Refutation found. Thanks to Tanya!
% 0.08/0.28 % SZS status Theorem for theBenchmark
% 0.08/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.28 % (604972)------------------------------
% 0.08/0.28 % (604972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.28 % (604972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.28 % (604972)CaDiCaL version: 2.1.3
% 0.08/0.28 % (604972)Termination reason: Refutation
% 0.08/0.28 % (604972)Time elapsed: 0.004 s
% 0.08/0.28 % (604972)Peak memory usage: 12 MB
% 0.08/0.28 % (604972)Instructions burned: 3 (million)
% 0.08/0.28 % (604964)Success in time 0.042 s
% 0.08/0.28 % Vampire exiting
%------------------------------------------------------------------------------