%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO007-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 09:53:13 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 19 unt; 2 def)
% Number of atoms : 107 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 103 ( 50 ~; 51 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| between(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ between(X0,X1,X3)
| ~ between(X0,X1,X2)
| X0 = X1
| between(X0,X2,X3)
| between(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',connectivity_for_betweeness) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
fof(f13,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
fof(f14,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
fof(f21,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).
fof(f22,axiom,
between(d,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_between_a_and_c) ).
fof(f23,axiom,
between(e,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_between_a_and_e) ).
fof(f24,axiom,
~ between(d,e,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_not_between_d_and_a) ).
fof(f25,negated_conjecture,
~ between(e,d,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_between_e_and_a) ).
fof(f86,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f14,f5]) ).
fof(f88,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f13,f86]) ).
fof(f99,plain,
! [X0] :
( ~ between(X0,d,c)
| between(X0,d,a) ),
inference(resolution,[],[f2,f22]) ).
fof(f100,plain,
! [X0] :
( ~ between(X0,e,c)
| between(X0,e,a) ),
inference(resolution,[],[f2,f23]) ).
fof(f1185,plain,
! [X2,X3,X0,X1] :
( ~ between(X0,X3,X1)
| ~ between(X0,X1,X2)
| outer_pasch(X3,X0,X0,X2,X1) = X0 ),
inference(resolution,[],[f7,f1]) ).
fof(f1809,plain,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| outer_pasch(X1,X0,X0,X2,X1) = X0 ),
inference(resolution,[],[f1185,f88]) ).
fof(f2199,plain,
d = outer_pasch(a,d,d,c,a),
inference(resolution,[],[f1809,f22]) ).
fof(f2200,plain,
e = outer_pasch(a,e,e,c,a),
inference(resolution,[],[f1809,f23]) ).
fof(f2207,plain,
( between(c,a,d)
| ~ between(d,a,c)
| ~ between(d,a,a) ),
inference(superposition,[],[f8,f2199]) ).
fof(f2209,plain,
( between(c,a,e)
| ~ between(e,a,c)
| ~ between(e,a,a) ),
inference(superposition,[],[f8,f2200]) ).
fof(f2459,plain,
( between(c,a,e)
| ~ between(e,a,a) ),
inference(forward_subsumption_resolution,[],[f2209,f23]) ).
fof(f2461,plain,
between(c,a,e),
inference(forward_subsumption_resolution,[],[f2459,f88]) ).
fof(f2473,plain,
! [X0] :
( ~ between(c,a,X0)
| a = c
| between(c,X0,e)
| between(c,e,X0) ),
inference(resolution,[],[f2461,f3]) ).
fof(f2477,plain,
! [X0] :
( ~ between(c,a,X0)
| between(c,X0,e)
| between(c,e,X0) ),
inference(forward_subsumption_resolution,[],[f2473,f21]) ).
fof(f2564,plain,
( between(c,a,d)
| ~ between(d,a,a) ),
inference(forward_subsumption_resolution,[],[f2207,f22]) ).
fof(f2566,plain,
between(c,a,d),
inference(forward_subsumption_resolution,[],[f2564,f88]) ).
fof(f2622,plain,
( between(c,d,e)
| between(c,e,d) ),
inference(resolution,[],[f2477,f2566]) ).
fof(f2629,definition,
( spl0_62
<=> between(c,e,d) ),
introduced(definition,[new_symbols(definition,[spl0_62])],[avatar_definition]) ).
fof(f2631,plain,
( between(c,e,d)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f2629]) ).
fof(f2633,definition,
( spl0_63
<=> between(c,d,e) ),
introduced(definition,[new_symbols(definition,[spl0_63])],[avatar_definition]) ).
fof(f2635,plain,
( between(c,d,e)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f2633]) ).
fof(f2636,plain,
( spl0_62
| spl0_63 ),
inference(avatar_split_clause,[],[f2622,f2633,f2629]) ).
fof(f2648,plain,
( c = outer_pasch(e,c,c,d,e)
| ~ spl0_62 ),
inference(resolution,[],[f2631,f1809]) ).
fof(f2664,plain,
( between(d,e,c)
| ~ between(c,e,d)
| ~ between(c,e,e)
| ~ spl0_62 ),
inference(superposition,[],[f8,f2648]) ).
fof(f2666,plain,
( between(d,e,c)
| ~ between(c,e,e)
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f2664,f2631]) ).
fof(f2667,plain,
( between(d,e,c)
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f2666,f88]) ).
fof(f2668,plain,
( between(d,e,a)
| ~ spl0_62 ),
inference(resolution,[],[f2667,f100]) ).
fof(f2673,plain,
( $false
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f2668,f24]) ).
fof(f2674,plain,
~ spl0_62,
inference(avatar_contradiction_clause,[],[f2673]) ).
fof(f2677,plain,
( c = outer_pasch(d,c,c,e,d)
| ~ spl0_63 ),
inference(resolution,[],[f2635,f1809]) ).
fof(f2680,plain,
( between(e,d,c)
| ~ between(c,d,e)
| ~ between(c,d,d)
| ~ spl0_63 ),
inference(superposition,[],[f8,f2677]) ).
fof(f2682,plain,
( between(e,d,c)
| ~ between(c,d,d)
| ~ spl0_63 ),
inference(forward_subsumption_resolution,[],[f2680,f2635]) ).
fof(f2683,plain,
( between(e,d,c)
| ~ spl0_63 ),
inference(forward_subsumption_resolution,[],[f2682,f88]) ).
fof(f2684,plain,
( between(e,d,a)
| ~ spl0_63 ),
inference(resolution,[],[f2683,f99]) ).
fof(f2689,plain,
( $false
| ~ spl0_63 ),
inference(forward_subsumption_resolution,[],[f2684,f25]) ).
fof(f2690,plain,
~ spl0_63,
inference(avatar_contradiction_clause,[],[f2689]) ).
cnf(s1443,plain,
( spl0_62
| spl0_63 ),
inference(sat_conversion,[],[f2636]) ).
cnf(s1469,plain,
~ spl0_62,
inference(sat_conversion,[],[f2674]) ).
cnf(s1485,plain,
~ spl0_63,
inference(sat_conversion,[],[f2690]) ).
cnf(s1486,plain,
$false,
inference(rat,[],[s1443,s1485,s1469]) ).
fof(f2691,plain,
$false,
inference(avatar_sat_refutation,[],[s1486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO007-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 06:31:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.47 % (3147186)Will run a generic schedule for satisfiability detection.
% 0.13/0.47 % (3147199)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2066783587:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.47 % (3147197)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2832147915_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.47 % (3147200)dis+10_1_sil=32000:sp=arity:random_seed=4006968306:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.47 % (3147198)% WARNING: option uhcvi not known.
% 0.13/0.47 % (3147201)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1019946354:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.47 % (3147203)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1891405759:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.47 % (3147202)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1865670332:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.47 % TRYING [1]
% 0.13/0.47 % TRYING [2]
% 0.13/0.47 % TRYING [3]
% 0.13/0.47 % (3147198)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3563352030:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.47 % (3147199) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3147186-3147199"...
% 0.13/0.47 % (3147199)...printing done.
% 0.13/0.47 % (3147199)Refutation found. Thanks to Tanya!
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.47 % (3147199)------------------------------
% 0.13/0.47 % (3147199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.47 % (3147199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.47 % (3147199)CaDiCaL version: 2.1.3
% 0.13/0.47 % (3147199)Termination reason: Refutation
% 0.13/0.47 % (3147199)Time elapsed: 0.033 s
% 0.13/0.47 % (3147199)Peak memory usage: 13 MB
% 0.13/0.47 % (3147199)Instructions burned: 87 (million)
% 0.13/0.47 % (3147186)Success in time 0.064 s
% 0.13/0.47 % Vampire exiting
%------------------------------------------------------------------------------