%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:51:20 AM UTC 2026
% Result : Unsatisfiable 3.61s 1.48s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 14 unt; 2 def)
% Number of atoms : 68 ( 4 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 64 ( 32 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-5 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f19,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f20,axiom,
between(u1,v1,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w) ).
fof(f21,axiom,
between(u,x,u1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_between_u_and_u1) ).
fof(f23,negated_conjecture,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion2) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( inner_pasch(X3,X0,X2,X1,X0) = X0
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[],[f8,f7]) ).
fof(f26,plain,
( ~ between(w,v,u)
| ~ between(v1,inner_pasch(u,x,u1,v1,w),u) ),
inference(resolution,[],[f9,f23]) ).
fof(f29,definition,
( spl0_1
<=> between(v1,inner_pasch(u,x,u1,v1,w),u) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f31,plain,
( ~ between(v1,inner_pasch(u,x,u1,v1,w),u)
| spl0_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl0_2
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f35,plain,
( ~ between(w,v,u)
| spl0_2 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f26,f33,f29]) ).
fof(f37,plain,
( ~ between(w,v1,u1)
| ~ between(u,x,u1)
| spl0_1 ),
inference(resolution,[],[f31,f9]) ).
fof(f38,plain,
( ~ between(w,v1,u1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f37,f21]) ).
fof(f39,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f41,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f39]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( between(X1,X0,X2)
| ~ between(X0,X1,X3)
| ~ between(X2,X0,X3)
| ~ between(X2,X0,X3)
| ~ between(X0,X1,X3) ),
inference(superposition,[],[f9,f24]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( between(X1,X0,X2)
| ~ between(X0,X1,X3)
| ~ between(X2,X0,X3) ),
inference(duplicate_literal_removal,[],[f62]) ).
fof(f152,plain,
( ! [X0] :
( ~ between(v1,w,X0)
| ~ between(u1,v1,X0) )
| spl0_1 ),
inference(resolution,[],[f65,f38]) ).
fof(f153,plain,
( ~ between(u1,v1,w)
| spl0_1 ),
inference(resolution,[],[f152,f41]) ).
fof(f158,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f153,f20]) ).
fof(f159,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f158]) ).
fof(f160,plain,
( ! [X0] :
( ~ between(v,w,X0)
| ~ between(u,v,X0) )
| spl0_2 ),
inference(resolution,[],[f35,f65]) ).
fof(f161,plain,
( ~ between(u,v,w)
| spl0_2 ),
inference(resolution,[],[f160,f41]) ).
fof(f166,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f161,f19]) ).
fof(f167,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f166]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f159]) ).
cnf(s6,plain,
spl0_2,
inference(sat_conversion,[],[f167]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5]) ).
fof(f168,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:45:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.61/1.48 % (1973166)Input is clausal, will run a generic CNF schedule.
% 3.61/1.48 % (1973172)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=604716679:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.61/1.48 % (1973174)lrs+10_1_sil=8000:sp=occurrence:random_seed=2809453940:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.61/1.48 % (1973171)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=3710534270:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.61/1.48 % (1973173)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4153103240:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.61/1.48 % (1973177)dis-21_1_sil=8000:lcm=predicate:random_seed=1815853817:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.61/1.48 % (1973175)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4181495890:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.61/1.48 % (1973176)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=435179492:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.61/1.48 % (1973174)Refutation not found, incomplete strategy
% 3.61/1.48 % (1973174)------------------------------
% 3.61/1.48 % (1973174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.48 % (1973175)Refutation not found, incomplete strategy
% 3.61/1.48 % (1973175)------------------------------
% 3.61/1.48 % (1973175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.48 % (1973175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.48 % (1973174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.48 % (1973175)CaDiCaL version: 2.1.3
% 3.61/1.48 % (1973174)CaDiCaL version: 2.1.3
% 3.61/1.48 % (1973175)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.48 % (1973175)Time elapsed: 0.001 s
% 3.61/1.48 % (1973174)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.48 % (1973174)Time elapsed: 0.001 s
% 3.61/1.48 % (1973174)Peak memory usage: 88 MB
% 3.61/1.48 % (1973175)Peak memory usage: 87 MB
% 3.61/1.48 % (1973177)Refutation not found, incomplete strategy
% 3.61/1.48 % (1973177)------------------------------
% 3.61/1.48 % (1973177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.48 % (1973177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.48 % (1973177)CaDiCaL version: 2.1.3
% 3.61/1.48 % (1973177)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.48 % (1973177)Time elapsed: 0.002 s
% 3.61/1.48 % (1973177)Peak memory usage: 88 MB
% 3.61/1.48 % (1973177)Instructions burned: 1 (million)
% 3.61/1.48 % (1973176)First to succeed.
% 3.61/1.48 % (1973176)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1973166"
% 3.61/1.48 % (1973174)------------------------------
% 3.61/1.48 % (1973174)------------------------------
% 3.61/1.48 % (1973175)------------------------------
% 3.61/1.48 % (1973175)------------------------------
% 3.61/1.48 % (1973177)------------------------------
% 3.61/1.48 % (1973177)------------------------------
% 3.61/1.48 % (1973176)Refutation found. Thanks to Tanya!
% 3.61/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.61/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.48 % (1973176)------------------------------
% 3.61/1.48 % (1973176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.48 % (1973176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.48 % (1973176)CaDiCaL version: 2.1.3
% 3.61/1.48 % (1973176)Termination reason: Refutation
% 3.61/1.48 % (1973176)Time elapsed: 0.009 s
% 3.61/1.48 % (1973176)Peak memory usage: 89 MB
% 3.61/1.48 % (1973176)Instructions burned: 9 (million)
% 3.61/1.48 % (1973176)------------------------------
% 3.61/1.48 % (1973176)------------------------------
% 3.61/1.48 % (1973166)Success in time 0.429 s
% 3.61/1.48 % Vampire exiting
%------------------------------------------------------------------------------