%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET794+4 : 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 12:41:56 PM UTC 2026
% Result : Theorem 2.68s 1.43s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 10 unt; 4 def)
% Number of atoms : 199 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 211 ( 80 ~; 88 |; 25 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 83 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( total_order(X0,X1)
<=> ( order(X0,X1)
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( apply(X0,X2,X3)
| apply(X0,X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_order) ).
fof(f6,axiom,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',least) ).
fof(f8,axiom,
! [X0,X1,X2] :
( min(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X3,X2) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',min) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( total_order(X0,X1)
& min(X2,X0,X1) )
=> least(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV6) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( total_order(X0,X1)
& min(X2,X0,X1) )
=> least(X2,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( min(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X3,X2) )
=> X2 = X3 ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) )
=> least(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( total_order(X0,X1)
=> ( order(X0,X1)
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( apply(X0,X2,X3)
| apply(X0,X3,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( ( order(X0,X1)
& ! [X2,X3] :
( apply(X0,X2,X3)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) ) )
| ~ total_order(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( order(X0,X1)
& ! [X2,X3] :
( apply(X0,X2,X3)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) ) )
| ~ total_order(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
| ~ min(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
| ~ min(X2,X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
? [X0,X1,X2] :
( ~ least(X2,X0,X1)
& total_order(X0,X1)
& min(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ~ least(X2,X0,X1)
& total_order(X0,X1)
& min(X2,X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| ( ~ apply(X0,X2,sK0(X0,X1,X2))
& member(sK0(X0,X1,X2),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f23]) ).
fof(f29,plain,
( ~ least(sK3,sK1,sK2)
& total_order(sK1,sK2)
& min(sK3,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f27]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ total_order(X0,X1)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X1)
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ apply(X0,X2,sK0(X0,X1,X2))
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ min(X2,X0,X1)
| ~ member(X3,X1)
| ~ apply(X0,X3,X2)
| X2 = X3 ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ min(X2,X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
min(sK3,sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
total_order(sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
~ least(sK3,sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
! [X0] :
( ~ apply(sK1,X0,sK3)
| ~ member(X0,sK2)
| sK3 = X0 ),
inference(resolution,[],[f37,f39]) ).
fof(f43,plain,
! [X0,X1] :
( ~ member(X1,sK2)
| apply(sK1,X0,X1)
| ~ member(X0,sK2)
| apply(sK1,X1,X0) ),
inference(resolution,[],[f33,f40]) ).
fof(f46,plain,
! [X2,X0,X1] :
( apply(sK1,X0,sK0(X1,sK2,X2))
| ~ member(X0,sK2)
| apply(sK1,sK0(X1,sK2,X2),X0)
| ~ member(X2,sK2)
| least(X2,X1,sK2) ),
inference(resolution,[],[f43,f35]) ).
fof(f47,plain,
! [X0] :
( ~ member(X0,sK2)
| apply(sK1,X0,X0)
| apply(sK1,X0,X0) ),
inference(factoring,[],[f43]) ).
fof(f48,plain,
! [X0] :
( apply(sK1,X0,X0)
| ~ member(X0,sK2) ),
inference(duplicate_literal_removal,[],[f47]) ).
fof(f56,plain,
! [X0] :
( ~ member(X0,sK2)
| apply(sK1,sK0(sK1,sK2,X0),X0)
| ~ member(X0,sK2)
| least(X0,sK1,sK2)
| ~ member(X0,sK2)
| least(X0,sK1,sK2) ),
inference(resolution,[],[f46,f36]) ).
fof(f57,plain,
! [X0] :
( least(X0,sK1,sK2)
| apply(sK1,sK0(sK1,sK2,X0),X0)
| ~ member(X0,sK2) ),
inference(duplicate_literal_removal,[],[f56]) ).
fof(f62,plain,
( apply(sK1,sK0(sK1,sK2,sK3),sK3)
| ~ member(sK3,sK2) ),
inference(resolution,[],[f57,f41]) ).
fof(f64,definition,
( spl4_1
<=> member(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f65,plain,
( member(sK3,sK2)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( ~ member(sK3,sK2)
| spl4_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl4_2
<=> apply(sK1,sK0(sK1,sK2,sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f70,plain,
( apply(sK1,sK0(sK1,sK2,sK3),sK3)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f62,f68,f64]) ).
fof(f73,plain,
( ! [X0] : ~ min(sK3,X0,sK2)
| spl4_1 ),
inference(resolution,[],[f66,f38]) ).
fof(f78,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f73,f39]) ).
fof(f79,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f78]) ).
fof(f87,plain,
( ~ member(sK0(sK1,sK2,sK3),sK2)
| sK3 = sK0(sK1,sK2,sK3)
| ~ spl4_2 ),
inference(resolution,[],[f70,f42]) ).
fof(f89,definition,
( spl4_3
<=> sK3 = sK0(sK1,sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f91,plain,
( sK3 = sK0(sK1,sK2,sK3)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f93,definition,
( spl4_4
<=> member(sK0(sK1,sK2,sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f95,plain,
( ~ member(sK0(sK1,sK2,sK3),sK2)
| spl4_4 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl4_3
| ~ spl4_4
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f87,f68,f93,f89]) ).
fof(f97,plain,
( ~ member(sK3,sK2)
| least(sK3,sK1,sK2)
| spl4_4 ),
inference(resolution,[],[f95,f35]) ).
fof(f99,plain,
( least(sK3,sK1,sK2)
| ~ spl4_1
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f97,f65]) ).
fof(f100,plain,
( $false
| ~ spl4_1
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f99,f41]) ).
fof(f101,plain,
( ~ spl4_1
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f105,plain,
( ~ apply(sK1,sK3,sK3)
| ~ member(sK3,sK2)
| least(sK3,sK1,sK2)
| ~ spl4_3 ),
inference(superposition,[],[f36,f91]) ).
fof(f107,plain,
( ~ member(sK3,sK2)
| least(sK3,sK1,sK2)
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f105,f48]) ).
fof(f108,plain,
( least(sK3,sK1,sK2)
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f107,f65]) ).
fof(f109,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f108,f41]) ).
fof(f110,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f109]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f71]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
( ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f96]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f110]) ).
cnf(s6,plain,
~ spl4_3,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
spl4_4,
inference(rat,[],[s4,s2]) ).
cnf(s8,plain,
~ spl4_2,
inference(rat,[],[s3,s7,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s2]) ).
fof(f111,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:52:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.68/1.43 % (4107429)Detected formulas, will run a generic FOF schedule.
% 2.68/1.43 % (4107449)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4201327060:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.43 % (4107449)First to succeed.
% 2.68/1.43 % (4107449)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4107429"
% 2.68/1.43 % (4107444)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=573138878:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.43 % (4107448)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1898865348:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.43 % (4107447)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2732521895:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.43 % (4107446)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=2487865833:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.43 % (4107450)dis-21_1_sil=8000:lcm=predicate:random_seed=1072715070: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)
% 2.68/1.43 % (4107445)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=831177559:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.43 % (4107447)Also succeeded, but the first one will report.
% 2.68/1.43 % (4107448)Also succeeded, but the first one will report.
% 2.68/1.43 % (4107450)Instruction limit reached!
% 2.68/1.43 % (4107450)------------------------------
% 2.68/1.43 % (4107450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.43 % (4107450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.43 % (4107450)CaDiCaL version: 2.1.3
% 2.68/1.43 % (4107450)Termination reason: Instruction limit
% 2.68/1.43 % (4107450)Termination phase: Saturation
% 2.68/1.43 % (4107450)Time elapsed: 0.057 s
% 2.68/1.43 % (4107450)Peak memory usage: 89 MB
% 2.68/1.43 % (4107450)Instructions burned: 129 (million)
% 2.68/1.43 % (4107449)Refutation found. Thanks to Tanya!
% 2.68/1.43 % SZS status Theorem for theBenchmark
% 2.68/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.43 % (4107449)------------------------------
% 2.68/1.43 % (4107449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.43 % (4107449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.43 % (4107449)CaDiCaL version: 2.1.3
% 2.68/1.43 % (4107449)Termination reason: Refutation
% 2.68/1.43 % (4107449)Time elapsed: 0.003 s
% 2.68/1.43 % (4107449)Peak memory usage: 89 MB
% 2.68/1.43 % (4107449)Instructions burned: 5 (million)
% 2.68/1.43 % (4107449)------------------------------
% 2.68/1.43 % (4107449)------------------------------
% 2.68/1.43 % (4107429)Success in time 0.274 s
% 2.68/1.43 % Vampire exiting
%------------------------------------------------------------------------------