%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 10:18:52 AM UTC 2026
% Result : Theorem 5.11s 1.94s
% Output : Refutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 17 unt; 7 def)
% Number of atoms : 154 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 160 ( 72 ~; 65 |; 12 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 56 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& ! [X3] :
( element(X3,X2)
=> ? [X4] :
( element(X4,X1)
& apply(X0,X4) = X3 ) ) )
=> surjection(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_surjection) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( element(X1,X0)
& element(X2,X0) )
=> element(subtract(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_in_domain) ).
fof(f19,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(f33,axiom,
! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( element(X1,b)
& element(X2,b)
& apply(g,subtract(b,X1,X2)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma12) ).
fof(f34,conjecture,
surjection(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_surjection) ).
fof(f35,negated_conjecture,
~ surjection(g),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f36,plain,
~ surjection(g),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0] :
( ? [X1,X2] :
( element(X1,b)
& element(X2,b)
& apply(g,subtract(b,X1,X2)) = X0 )
| ~ element(X0,e) ),
inference(ennf_transformation,[],[f33]) ).
fof(f50,plain,
! [X0,X1,X2] :
( surjection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ element(X4,X1)
| apply(X0,X4) != X3 )
& element(X3,X2) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0,X1,X2] :
( surjection(X0)
| ~ morphism(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ element(X4,X1)
| apply(X0,X4) != X3 )
& element(X3,X2) ) ),
inference(flattening,[],[f50]) ).
fof(f62,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f63,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f62]) ).
fof(f66,plain,
! [X0] :
( ( element(sK5(X0),b)
& element(sK6(X0),b)
& apply(g,subtract(b,sK5(X0),sK6(X0))) = X0 )
| ~ element(X0,e) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f39]) ).
fof(f76,plain,
! [X0,X1,X2] :
( surjection(X0)
| ~ morphism(X0,X1,X2)
| ( ! [X4] :
( ~ element(X4,X1)
| apply(X0,X4) != sK11(X0,X1,X2) )
& element(sK11(X0,X1,X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f51]) ).
fof(f84,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f19]) ).
fof(f107,plain,
! [X0] :
( apply(g,subtract(b,sK5(X0),sK6(X0))) = X0
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f66]) ).
fof(f108,plain,
! [X0] :
( element(sK6(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f66]) ).
fof(f109,plain,
! [X0] :
( element(sK5(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f66]) ).
fof(f110,plain,
~ surjection(g),
inference(cnf_transformation,[],[f36]) ).
fof(f124,plain,
! [X2,X0,X1] :
( surjection(X0)
| ~ morphism(X0,X1,X2)
| element(sK11(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( surjection(X0)
| ~ morphism(X0,X1,X2)
| ~ element(X4,X1)
| apply(X0,X4) != sK11(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f137,plain,
! [X2,X0,X1] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f140,definition,
! [X0,X1] :
( sQ15_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ15_eqProxy])],[equality_proxy_definition]) ).
fof(f147,plain,
! [X0] :
( sQ15_eqProxy(apply(g,subtract(b,sK5(X0),sK6(X0))),X0)
| ~ element(X0,e) ),
inference(equality_proxy_replacement,[],[f107,f140]) ).
fof(f158,plain,
! [X2,X0,X1,X4] :
( ~ sQ15_eqProxy(apply(X0,X4),sK11(X0,X1,X2))
| ~ morphism(X0,X1,X2)
| ~ element(X4,X1)
| surjection(X0) ),
inference(equality_proxy_replacement,[],[f125,f140]) ).
fof(f168,plain,
! [X0,X1] :
( ~ morphism(g,X0,X1)
| element(sK11(g,X0,X1),X1) ),
inference(resolution,[],[f124,f110]) ).
fof(f176,plain,
element(sK11(g,b,e),e),
inference(resolution,[],[f168,f84]) ).
fof(f184,plain,
! [X0,X1] :
( ~ morphism(g,X0,X1)
| ~ element(subtract(b,sK5(sK11(g,X0,X1)),sK6(sK11(g,X0,X1))),X0)
| surjection(g)
| ~ element(sK11(g,X0,X1),e) ),
inference(resolution,[],[f158,f147]) ).
fof(f187,definition,
( spl16_1
<=> surjection(g) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f188,plain,
( surjection(g)
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,definition,
( spl16_2
<=> ! [X0,X1] :
( ~ morphism(g,X0,X1)
| ~ element(sK11(g,X0,X1),e)
| ~ element(subtract(b,sK5(sK11(g,X0,X1)),sK6(sK11(g,X0,X1))),X0) ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f191,plain,
( ! [X0,X1] :
( ~ morphism(g,X0,X1)
| ~ element(sK11(g,X0,X1),e)
| ~ element(subtract(b,sK5(sK11(g,X0,X1)),sK6(sK11(g,X0,X1))),X0) )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f192,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f184,f190,f187]) ).
fof(f193,plain,
( ~ element(sK11(g,b,e),e)
| ~ element(subtract(b,sK5(sK11(g,b,e)),sK6(sK11(g,b,e))),b)
| ~ spl16_2 ),
inference(resolution,[],[f191,f84]) ).
fof(f195,definition,
( spl16_3
<=> element(subtract(b,sK5(sK11(g,b,e)),sK6(sK11(g,b,e))),b) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f196,plain,
( ~ element(subtract(b,sK5(sK11(g,b,e)),sK6(sK11(g,b,e))),b)
| spl16_3 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,definition,
( spl16_4
<=> element(sK11(g,b,e),e) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f199,plain,
( ~ element(sK11(g,b,e),e)
| spl16_4 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( ~ spl16_3
| ~ spl16_4
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f193,f190,f198,f195]) ).
fof(f201,plain,
( ~ element(sK5(sK11(g,b,e)),b)
| ~ element(sK6(sK11(g,b,e)),b)
| spl16_3 ),
inference(resolution,[],[f196,f137]) ).
fof(f203,definition,
( spl16_5
<=> element(sK6(sK11(g,b,e)),b) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
fof(f204,plain,
( ~ element(sK6(sK11(g,b,e)),b)
| spl16_5 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f206,definition,
( spl16_6
<=> element(sK5(sK11(g,b,e)),b) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
fof(f207,plain,
( ~ element(sK5(sK11(g,b,e)),b)
| spl16_6 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f208,plain,
( ~ spl16_5
| ~ spl16_6
| spl16_3 ),
inference(avatar_split_clause,[],[f201,f195,f206,f203]) ).
fof(f209,plain,
( ~ element(sK11(g,b,e),e)
| spl16_5 ),
inference(resolution,[],[f204,f108]) ).
fof(f210,plain,
( ~ spl16_4
| spl16_5 ),
inference(avatar_split_clause,[],[f209,f203,f198]) ).
fof(f211,plain,
( $false
| spl16_4 ),
inference(resolution,[],[f199,f176]) ).
fof(f212,plain,
spl16_4,
inference(avatar_contradiction_clause,[],[f211]) ).
fof(f213,plain,
( ~ element(sK11(g,b,e),e)
| spl16_6 ),
inference(resolution,[],[f207,f109]) ).
fof(f214,plain,
( ~ spl16_4
| spl16_6 ),
inference(avatar_split_clause,[],[f213,f206,f198]) ).
fof(f215,plain,
( $false
| ~ spl16_1 ),
inference(resolution,[],[f188,f110]) ).
fof(f217,plain,
~ spl16_1,
inference(avatar_contradiction_clause,[],[f215]) ).
cnf(s1,plain,
( spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f192]) ).
cnf(s2,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_4 ),
inference(sat_conversion,[],[f200]) ).
cnf(s3,plain,
( spl16_3
| ~ spl16_5
| ~ spl16_6 ),
inference(sat_conversion,[],[f208]) ).
cnf(s4,plain,
( ~ spl16_4
| spl16_5 ),
inference(sat_conversion,[],[f210]) ).
cnf(s5,plain,
spl16_4,
inference(sat_conversion,[],[f212]) ).
cnf(s6,plain,
( ~ spl16_4
| spl16_6 ),
inference(sat_conversion,[],[f214]) ).
cnf(s7,plain,
~ spl16_1,
inference(sat_conversion,[],[f217]) ).
cnf(s8,plain,
spl16_6,
inference(rat,[],[s6,s5]) ).
cnf(s9,plain,
spl16_5,
inference(rat,[],[s4,s5]) ).
cnf(s10,plain,
spl16_3,
inference(rat,[],[s3,s8,s9]) ).
cnf(s11,plain,
~ spl16_2,
inference(rat,[],[s2,s5,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s7]) ).
fof(f218,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n007.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 10:46:55 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 5.11/1.94 % (1231198)Detected formulas, will run a generic FOF schedule.
% 5.11/1.94 % (1231209)dis-21_1_sil=8000:lcm=predicate:random_seed=3721265546: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)
% 5.11/1.94 % (1231209)First to succeed.
% 5.11/1.94 % (1231209)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1231198"
% 5.11/1.94 % (1231208)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1908771277:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.11/1.94 % (1231204)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=3287985809:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.11/1.94 % (1231203)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=134366820:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.11/1.94 % (1231206)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3727000089:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.11/1.94 % (1231205)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=2183926128:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.11/1.94 % (1231206)Refutation not found, incomplete strategy
% 5.11/1.94 % (1231206)------------------------------
% 5.11/1.94 % (1231206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.94 % (1231206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.94 % (1231206)CaDiCaL version: 2.1.3
% 5.11/1.94 % (1231206)Termination reason: Refutation not found, incomplete strategy
% 5.11/1.94 % (1231206)Time elapsed: 0.001 s
% 5.11/1.94 % (1231206)Peak memory usage: 87 MB
% 5.11/1.94 % (1231208)Also succeeded, but the first one will report.
% 5.11/1.94 % (1231207)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1878788120:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.11/1.94 % (1231207)Refutation not found, incomplete strategy
% 5.11/1.94 % (1231207)------------------------------
% 5.11/1.94 % (1231207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.94 % (1231207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.94 % (1231207)CaDiCaL version: 2.1.3
% 5.11/1.94 % (1231207)Termination reason: Refutation not found, incomplete strategy
% 5.11/1.94 % (1231207)Time elapsed: 0.001 s
% 5.11/1.94 % (1231207)Peak memory usage: 87 MB
% 5.11/1.94 % (1231209)Refutation found. Thanks to Tanya!
% 5.11/1.94 % SZS status Theorem for theBenchmark
% 5.11/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 5.11/1.94 % (1231209)------------------------------
% 5.11/1.94 % (1231209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.94 % (1231209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.94 % (1231209)CaDiCaL version: 2.1.3
% 5.11/1.94 % (1231209)Termination reason: Refutation
% 5.11/1.94 % (1231209)Time elapsed: 0.006 s
% 5.11/1.94 % (1231209)Peak memory usage: 89 MB
% 5.11/1.94 % (1231209)Instructions burned: 6 (million)
% 5.11/1.94 % (1231209)------------------------------
% 5.11/1.94 % (1231209)------------------------------
% 5.11/1.94 % (1231198)Success in time 0.598 s
% 5.11/1.94 % Vampire exiting
%------------------------------------------------------------------------------