%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n002.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 09:39:21 AM UTC 2026
% Result : Theorem 3.51s 1.27s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 15 unt; 5 def)
% Number of atoms : 172 ( 18 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 195 ( 93 ~; 85 |; 7 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 60 !; 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,
! [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))],[f17]) ).
fof(f19,plain,
reflexive_rewrite(a,c),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
reflexive_rewrite(a,b),
inference(cnf_transformation,[],[f1]) ).
fof(f21,plain,
! [X0] :
( goal
| ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0,X1] :
( reflexive_rewrite(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X0,X1] :
( ~ rewrite(X0,X1)
| reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( rewrite(X0,X1)
| X0 = X1
| ~ reflexive_rewrite(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X2,X0,X1] :
( rewrite(X2,sK0(X1,X2))
| ~ rewrite(X0,X1)
| ~ rewrite(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X2,X0,X1] :
( rewrite(X1,sK0(X1,X2))
| ~ rewrite(X0,X1)
| ~ rewrite(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
~ goal,
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X1] : reflexive_rewrite(X1,X1),
inference(equality_resolution,[],[f22]) ).
fof(f30,definition,
( spl1_1
<=> ! [X0] :
( ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(c,X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f31,plain,
( ! [X0] :
( ~ reflexive_rewrite(c,X0)
| ~ reflexive_rewrite(b,X0) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f33,definition,
( spl1_2
<=> goal ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f36,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f21,f33,f30]) ).
fof(f37,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f27,f33]) ).
fof(f38,plain,
( ~ reflexive_rewrite(b,c)
| ~ spl1_1 ),
inference(resolution,[],[f28,f31]) ).
fof(f40,plain,
! [X2,X0,X1] :
( reflexive_rewrite(X2,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(resolution,[],[f25,f23]) ).
fof(f41,plain,
! [X2,X0,X1] :
( reflexive_rewrite(X1,sK0(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(resolution,[],[f26,f23]) ).
fof(f42,plain,
( ! [X0,X1] :
( ~ reflexive_rewrite(b,sK0(X1,c))
| ~ rewrite(X0,X1)
| ~ rewrite(X0,c) )
| ~ spl1_1 ),
inference(resolution,[],[f40,f31]) ).
fof(f44,plain,
( ! [X0,X1] :
( ~ rewrite(X0,b)
| ~ rewrite(X0,c)
| ~ rewrite(X1,c)
| ~ rewrite(X1,b) )
| ~ spl1_1 ),
inference(resolution,[],[f42,f41]) ).
fof(f46,definition,
( spl1_3
<=> ! [X1] :
( ~ rewrite(X1,c)
| ~ rewrite(X1,b) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f47,plain,
( ! [X1] :
( ~ rewrite(X1,c)
| ~ rewrite(X1,b) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl1_3
| spl1_3
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f44,f30,f46,f46]) ).
fof(f49,plain,
( ! [X0] :
( ~ rewrite(X0,b)
| c = X0
| ~ reflexive_rewrite(X0,c) )
| ~ spl1_3 ),
inference(resolution,[],[f47,f24]) ).
fof(f51,plain,
( ! [X0] :
( ~ reflexive_rewrite(X0,c)
| c = X0
| b = X0
| ~ reflexive_rewrite(X0,b) )
| ~ spl1_3 ),
inference(resolution,[],[f49,f24]) ).
fof(f52,plain,
( a = c
| a = b
| ~ reflexive_rewrite(a,b)
| ~ spl1_3 ),
inference(resolution,[],[f51,f19]) ).
fof(f54,plain,
( a = c
| a = b
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f52,f20]) ).
fof(f56,definition,
( spl1_4
<=> a = b ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f58,plain,
( a = b
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl1_5
<=> a = c ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f62,plain,
( a = c
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( spl1_4
| spl1_5
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f54,f46,f60,f56]) ).
fof(f65,plain,
( ! [X0] :
( ~ reflexive_rewrite(b,X0)
| ~ reflexive_rewrite(a,X0) )
| ~ spl1_1
| ~ spl1_5 ),
inference(superposition,[],[f31,f62]) ).
fof(f71,plain,
( ~ reflexive_rewrite(a,b)
| ~ spl1_1
| ~ spl1_5 ),
inference(resolution,[],[f65,f28]) ).
fof(f74,plain,
( $false
| ~ spl1_1
| ~ spl1_5 ),
inference(forward_subsumption_resolution,[],[f71,f20]) ).
fof(f75,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f74]) ).
fof(f77,plain,
( ~ reflexive_rewrite(a,c)
| ~ spl1_1
| ~ spl1_4 ),
inference(superposition,[],[f38,f58]) ).
fof(f81,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_subsumption_resolution,[],[f77,f19]) ).
fof(f82,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f81]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
( spl1_3
| ~ spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
( ~ spl1_1
| spl1_3 ),
inference(rat,[],[s3]) ).
cnf(s5,plain,
( ~ spl1_3
| spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f63]) ).
cnf(s6,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f75]) ).
cnf(s7,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s8,plain,
spl1_1,
inference(rat,[],[s1,s2]) ).
cnf(s9,plain,
~ spl1_4,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
~ spl1_5,
inference(rat,[],[s6,s8]) ).
cnf(s11,plain,
spl1_3,
inference(rat,[],[s4,s8]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s5,s10,s9,s11]) ).
fof(f83,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM007+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n002.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 21:46:38 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 3.51/1.27 % (806839)Detected formulas, will run a generic FOF schedule.
% 3.51/1.27 % (806850)dis-21_1_sil=8000:lcm=predicate:random_seed=1363632703: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)
% 3.51/1.27 % (806844)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=70951985:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.27 % (806850)Instruction limit reached!
% 3.51/1.27 % (806850)------------------------------
% 3.51/1.27 % (806850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.27 % (806850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.27 % (806850)CaDiCaL version: 2.1.3
% 3.51/1.27 % (806850)Termination reason: Instruction limit
% 3.51/1.27 % (806850)Termination phase: Saturation
% 3.51/1.27 % (806850)Time elapsed: 0.036 s
% 3.51/1.27 % (806850)Peak memory usage: 89 MB
% 3.51/1.27 % (806850)Instructions burned: 132 (million)
% 3.51/1.27 % (806849)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4045136061:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.27 % (806849)First to succeed.
% 3.51/1.27 % (806848)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1637530743:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.27 % (806847)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3598836770:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.27 % (806845)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=3524091609:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.27 % (806846)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=1492903234:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.27 % (806849)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-806839"
% 3.51/1.27 % (806848)Refutation not found, incomplete strategy
% 3.51/1.27 % (806848)------------------------------
% 3.51/1.27 % (806848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.27 % (806848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.27 % (806848)CaDiCaL version: 2.1.3
% 3.51/1.27 % (806848)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.27 % (806848)Time elapsed: 0.0000 s
% 3.51/1.27 % (806848)Peak memory usage: 86 MB
% 3.51/1.27 % (806847)Refutation not found, incomplete strategy
% 3.51/1.27 % (806847)------------------------------
% 3.51/1.27 % (806847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.27 % (806847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.27 % (806847)CaDiCaL version: 2.1.3
% 3.51/1.27 % (806847)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.27 % (806847)Time elapsed: 0.0000 s
% 3.51/1.27 % (806847)Peak memory usage: 87 MB
% 3.51/1.27 % (806854)lrs+10_1_sil=8000:sp=occurrence:random_seed=1667830265:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.51/1.27 % (806854)Also succeeded, but the first one will report.
% 3.51/1.27 % (806848)------------------------------
% 3.51/1.27 % (806848)------------------------------
% 3.51/1.27 % (806847)------------------------------
% 3.51/1.27 % (806847)------------------------------
% 3.51/1.27 % (806849)Refutation found. Thanks to Tanya!
% 3.51/1.27 % SZS status Theorem for theBenchmark
% 3.51/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.27 % (806849)------------------------------
% 3.51/1.27 % (806849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.27 % (806849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.27 % (806849)CaDiCaL version: 2.1.3
% 3.51/1.27 % (806849)Termination reason: Refutation
% 3.51/1.27 % (806849)Time elapsed: 0.004 s
% 3.51/1.27 % (806849)Peak memory usage: 89 MB
% 3.51/1.27 % (806849)Instructions burned: 3 (million)
% 3.51/1.27 % (806849)------------------------------
% 3.51/1.27 % (806849)------------------------------
% 3.51/1.27 % (806839)Success in time 0.409 s
% 3.51/1.27 % Vampire exiting
%------------------------------------------------------------------------------