%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 20 unt; 6 def)
% Number of atoms : 198 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 190 ( 76 ~; 97 |; 6 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 65 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
fof(f2,axiom,
! [X0] :
( ( reflexive_rewrite(b,X0)
& reflexive_rewrite(c,X0) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_ax) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
=> reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_in_reflexive_rewrite) ).
fof(f4,axiom,
! [X0,X1] :
( rewrite(X0,X1)
=> reflexive_rewrite(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(f5,axiom,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
=> ( X0 = X1
| rewrite(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_or_rewrite) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( rewrite(X0,X1)
& rewrite(X0,X2) )
=> ? [X3] :
( rewrite(X1,X3)
& rewrite(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_diamond) ).
fof(f7,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f8,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
~ goal,
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f11,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| ~ rewrite(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| rewrite(X0,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f15,plain,
! [X0,X1] :
( X0 = X1
| rewrite(X0,X1)
| ~ reflexive_rewrite(X0,X1) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ? [X3] :
( rewrite(X1,X3)
& rewrite(X2,X3) )
| ~ rewrite(X0,X1)
| ~ rewrite(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ? [X3] :
( rewrite(X1,X3)
& rewrite(X2,X3) )
| ~ rewrite(X0,X1)
| ~ rewrite(X0,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X0] :
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0)
| goal ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X0,X1] :
( X0 != X1
| reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( ~ rewrite(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X0,X1] :
( ~ reflexive_rewrite(X0,X1)
| rewrite(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| rewrite(X2,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ rewrite(X0,X2)
| ~ rewrite(X0,X1)
| rewrite(X1,sK0(X1,X2)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
~ goal,
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X1] : reflexive_rewrite(X1,X1),
inference(equality_resolution,[],[f21]) ).
fof(f28,plain,
~ reflexive_rewrite(a,b),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f29,plain,
~ reflexive_rewrite(a,c),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f30,plain,
! [X0] :
( reflexive_rewrite(c,X0)
| reflexive_rewrite(b,X0)
| ~ goal ),
inference(consistent_polarity_flipping,[],[f20]) ).
fof(f31,plain,
! [X1] : ~ reflexive_rewrite(X1,X1),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f32,plain,
! [X0,X1] :
( ~ reflexive_rewrite(X0,X1)
| rewrite(X0,X1) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( ~ rewrite(X0,X1)
| reflexive_rewrite(X0,X1)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ rewrite(X1,sK0(X1,X2))
| rewrite(X0,X1)
| rewrite(X0,X2) ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ rewrite(X2,sK0(X1,X2))
| rewrite(X0,X1)
| rewrite(X0,X2) ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f36,plain,
goal,
inference(consistent_polarity_flipping,[],[f26]) ).
fof(f38,definition,
( spl1_1
<=> goal ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f42,definition,
( spl1_2
<=> ! [X0] :
( reflexive_rewrite(c,X0)
| reflexive_rewrite(b,X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f43,plain,
( ! [X0] :
( reflexive_rewrite(c,X0)
| reflexive_rewrite(b,X0) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f30,f42,f38]) ).
fof(f45,plain,
spl1_1,
inference(avatar_split_clause,[],[f36,f38]) ).
fof(f46,plain,
( reflexive_rewrite(b,c)
| ~ spl1_2 ),
inference(resolution,[],[f43,f31]) ).
fof(f47,plain,
( ! [X0] :
( reflexive_rewrite(b,X0)
| rewrite(c,X0) )
| ~ spl1_2 ),
inference(resolution,[],[f43,f32]) ).
fof(f49,plain,
( rewrite(c,b)
| ~ spl1_2 ),
inference(resolution,[],[f47,f31]) ).
fof(f50,plain,
( ! [X0] :
( rewrite(c,X0)
| rewrite(b,X0) )
| ~ spl1_2 ),
inference(resolution,[],[f47,f32]) ).
fof(f64,plain,
( ! [X0,X1] :
( rewrite(b,sK0(X0,c))
| rewrite(X1,X0)
| rewrite(X1,c) )
| ~ spl1_2 ),
inference(resolution,[],[f50,f35]) ).
fof(f84,definition,
( spl1_7
<=> ! [X1] :
( rewrite(X1,c)
| rewrite(X1,b) ) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f85,plain,
( ! [X1] :
( rewrite(X1,c)
| rewrite(X1,b) )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( ! [X0,X1] :
( rewrite(X0,b)
| rewrite(X0,c)
| rewrite(X1,b)
| rewrite(X1,c) )
| ~ spl1_2 ),
inference(resolution,[],[f64,f34]) ).
fof(f95,plain,
( spl1_7
| spl1_7
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f87,f42,f84,f84]) ).
fof(f140,definition,
( spl1_8
<=> ! [X0] :
( rewrite(X0,b)
| c = X0
| reflexive_rewrite(X0,c) ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f141,plain,
( ! [X0] :
( reflexive_rewrite(X0,c)
| c = X0
| rewrite(X0,b) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f201,plain,
( ! [X0] :
( rewrite(X0,b)
| reflexive_rewrite(X0,c)
| c = X0 )
| ~ spl1_7 ),
inference(resolution,[],[f85,f33]) ).
fof(f202,plain,
( spl1_8
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f201,f84,f140]) ).
fof(f242,plain,
( a = c
| rewrite(a,b)
| ~ spl1_8 ),
inference(resolution,[],[f141,f29]) ).
fof(f246,definition,
( spl1_13
<=> rewrite(a,b) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f247,plain,
( ~ rewrite(a,b)
| spl1_13 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( rewrite(a,b)
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl1_14
<=> a = c ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f252,plain,
( a = c
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( spl1_13
| spl1_14
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f242,f140,f250,f246]) ).
fof(f276,plain,
( reflexive_rewrite(a,b)
| a = b
| ~ spl1_13 ),
inference(resolution,[],[f248,f33]) ).
fof(f277,plain,
( a = b
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f276,f28]) ).
fof(f279,plain,
( reflexive_rewrite(a,c)
| ~ spl1_2
| ~ spl1_13 ),
inference(superposition,[],[f46,f277]) ).
fof(f299,plain,
( $false
| ~ spl1_2
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f279,f29]) ).
fof(f300,plain,
( ~ spl1_2
| ~ spl1_13 ),
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f307,plain,
( rewrite(a,b)
| ~ spl1_2
| ~ spl1_14 ),
inference(superposition,[],[f49,f252]) ).
fof(f338,plain,
( $false
| ~ spl1_2
| spl1_13
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f307,f247]) ).
fof(f339,plain,
( ~ spl1_2
| spl1_13
| ~ spl1_14 ),
inference(avatar_contradiction_clause,[],[f338]) ).
cnf(s1,plain,
( ~ spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
spl1_1,
inference(sat_conversion,[],[f45]) ).
cnf(s8,plain,
( spl1_7
| ~ spl1_2
| spl1_7 ),
inference(sat_conversion,[],[f95]) ).
cnf(s9,plain,
( ~ spl1_2
| spl1_7 ),
inference(rat,[],[s8]) ).
cnf(s21,plain,
( ~ spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f202]) ).
cnf(s23,plain,
( ~ spl1_8
| spl1_13
| spl1_14 ),
inference(sat_conversion,[],[f253]) ).
cnf(s24,plain,
( ~ spl1_2
| ~ spl1_13 ),
inference(sat_conversion,[],[f300]) ).
cnf(s26,plain,
( ~ spl1_2
| spl1_13
| ~ spl1_14 ),
inference(sat_conversion,[],[f339]) ).
cnf(s27,plain,
spl1_2,
inference(rat,[],[s1,s2]) ).
cnf(s28,plain,
~ spl1_13,
inference(rat,[],[s24,s27]) ).
cnf(s30,plain,
spl1_7,
inference(rat,[],[s9,s27]) ).
cnf(s31,plain,
~ spl1_14,
inference(rat,[],[s26,s27,s28]) ).
cnf(s32,plain,
~ spl1_8,
inference(rat,[],[s23,s31,s28]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s21,s32,s30]) ).
fof(f340,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:46:42 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.07/0.26 % (112060)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (112066)% WARNING: option uhcvi not known.
% 0.07/0.26 % (112066)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3152909172:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.26 % (112066) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-112060-112066"...
% 0.07/0.26 % (112066)...printing done.
% 0.07/0.26 % (112065)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=181349226_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.26 % (112067)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4167392409:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.26 % (112068)dis+10_1_sil=32000:sp=arity:random_seed=227278695:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.26 % (112066)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (112066)------------------------------
% 0.07/0.26 % (112066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (112066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (112066)CaDiCaL version: 2.1.3
% 0.07/0.26 % (112066)Termination reason: Refutation
% 0.07/0.26 % (112066)Time elapsed: 0.005 s
% 0.07/0.26 % (112066)Peak memory usage: 12 MB
% 0.07/0.26 % (112066)Instructions burned: 11 (million)
% 0.07/0.26 % (112060)Success in time 0.029 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------