%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO507+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:52:49 AM UTC 2026
% Result : Theorem 5.15s 1.79s
% Output : Refutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 14 unt; 1 def)
% Number of atoms : 127 ( 24 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 153 ( 68 ~; 64 |; 20 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-5 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 70 ( 0 sgn 66 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,axiom,
! [X0,X1,X2] :
( ~ s_col(X0,X1,X2)
| s_col(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_11a) ).
fof(f46,axiom,
! [X0,X1] : s_col(X0,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz4_12b) ).
fof(f124,axiom,
! [X0,X1] :
( ~ s_r(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_8) ).
fof(f129,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ perpAt(X0,X1,X2,X3,X4)
| X0 != X1 )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| X3 != X4 )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| s_col(X3,X4,X2) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| s_col(X0,X1,X2) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| s_col(X0,X1,f813(X0,X1,X3,X4,X2)) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| s_col(X3,X4,g813(X0,X1,X3,X4,X2)) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| X2 != f813(X0,X1,X3,X4,X2) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| X2 != g813(X0,X1,X3,X4,X2) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| s_r(f813(X0,X1,X3,X4,X2),X2,g813(X0,X1,X3,X4,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_13a) ).
fof(f131,conjecture,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| ~ s_col(X0,X1,X2)
| ~ s_col(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_14a) ).
fof(f132,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| ~ s_col(X0,X1,X2)
| ~ s_col(X0,X1,X3) ),
inference(negated_conjecture,[status(cth)],[f131]) ).
fof(f144,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ~ perpAt(X0,X1,X2,X3,X4)
| s_col(X0,X1,X2) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| s_col(X3,X4,X2) )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| X0 != X1 )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| X3 != X4 )
& ( ~ perpAt(X0,X1,X2,X3,X4)
| ~ s_col(X0,X1,X5)
| ~ s_col(X3,X4,X6)
| s_r(X5,X2,X6) )
& ( perpAt(X0,X1,X2,X3,X4)
| X0 = X1
| X3 = X4
| ~ s_col(X0,X1,X2)
| ~ s_col(X3,X4,X2)
| s_col(X0,X1,f811(X0,X1,X3,X4,X2)) )
& ( perpAt(X0,X1,X2,X3,X4)
| X0 = X1
| X3 = X4
| ~ s_col(X0,X1,X2)
| ~ s_col(X3,X4,X2)
| s_col(X3,X4,g811(X0,X1,X3,X4,X2)) )
& ( perpAt(X0,X1,X2,X3,X4)
| X0 = X1
| X3 = X4
| ~ s_col(X0,X1,X2)
| ~ s_col(X3,X4,X2)
| ~ s_r(f811(X0,X1,X3,X4,X2),X2,g811(X0,X1,X3,X4,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn8_11a) ).
fof(f145,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ perp(X0,X1,X2,X3)
| perpAt(X0,X1,il(X0,X1,X2,X3),X2,X3) )
& ( perp(X0,X1,X2,X3)
| ~ perpAt(X0,X1,X4,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn8_11b) ).
fof(f146,plain,
? [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
& s_col(X0,X1,X2)
& s_col(X0,X1,X3) ),
inference(ennf_transformation,[],[f132]) ).
fof(f147,plain,
( perp(sK0,sK1,sK2,sK3)
& s_col(sK0,sK1,sK2)
& s_col(sK0,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f146]) ).
fof(f193,plain,
! [X2,X0,X1] :
( s_col(X1,X2,X0)
| ~ s_col(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f199,plain,
! [X0,X1] : s_col(X0,X1,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f285,plain,
! [X0,X1] :
( ~ s_r(X0,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f297,plain,
! [X2,X3,X0,X1,X4] :
( ~ perpAt(X0,X1,X2,X3,X4)
| X3 != X4 ),
inference(cnf_transformation,[],[f129]) ).
fof(f300,plain,
s_col(sK0,sK1,sK3),
inference(cnf_transformation,[],[f147]) ).
fof(f301,plain,
s_col(sK0,sK1,sK2),
inference(cnf_transformation,[],[f147]) ).
fof(f302,plain,
perp(sK0,sK1,sK2,sK3),
inference(cnf_transformation,[],[f147]) ).
fof(f354,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ perpAt(X0,X1,X2,X3,X4)
| ~ s_col(X0,X1,X5)
| ~ s_col(X3,X4,X6)
| s_r(X5,X2,X6) ),
inference(cnf_transformation,[],[f144]) ).
fof(f360,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perpAt(X0,X1,il(X0,X1,X2,X3),X2,X3) ),
inference(cnf_transformation,[],[f145]) ).
fof(f368,plain,
! [X2,X0,X1,X4] : ~ perpAt(X0,X1,X2,X4,X4),
inference(equality_resolution,[],[f297]) ).
fof(f428,plain,
perpAt(sK0,sK1,il(sK0,sK1,sK2,sK3),sK2,sK3),
inference(resolution,[],[f360,f302]) ).
fof(f486,plain,
! [X0,X1] :
( s_r(X0,il(sK0,sK1,sK2,sK3),X1)
| ~ s_col(sK2,sK3,X1)
| ~ s_col(sK0,sK1,X0) ),
inference(resolution,[],[f354,f428]) ).
fof(f487,plain,
! [X0] :
( ~ s_col(sK2,sK3,X0)
| ~ s_col(sK0,sK1,X0)
| il(sK0,sK1,sK2,sK3) = X0 ),
inference(resolution,[],[f486,f285]) ).
fof(f496,plain,
( ~ s_col(sK0,sK1,sK2)
| sK2 = il(sK0,sK1,sK2,sK3) ),
inference(resolution,[],[f487,f199]) ).
fof(f509,definition,
( spl4_1
<=> sK2 = sK3 ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f510,plain,
( sK2 != sK3
| spl4_1 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f511,plain,
( sK2 = sK3
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f516,plain,
sK2 = il(sK0,sK1,sK2,sK3),
inference(forward_subsumption_resolution,[],[f496,f301]) ).
fof(f518,plain,
! [X0,X1] :
( s_r(X0,sK2,X1)
| ~ s_col(sK2,sK3,X1)
| ~ s_col(sK0,sK1,X0) ),
inference(superposition,[],[f486,f516]) ).
fof(f530,plain,
! [X0] :
( ~ s_col(sK2,sK3,X0)
| ~ s_col(sK0,sK1,X0)
| sK2 = X0 ),
inference(resolution,[],[f518,f285]) ).
fof(f550,plain,
( perpAt(sK0,sK1,il(sK0,sK1,sK2,sK2),sK2,sK2)
| ~ spl4_1 ),
inference(superposition,[],[f428,f511]) ).
fof(f561,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f550,f368]) ).
fof(f562,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f561]) ).
fof(f574,plain,
! [X0] :
( ~ s_col(X0,sK2,sK3)
| sK2 = X0
| ~ s_col(sK0,sK1,X0) ),
inference(resolution,[],[f530,f193]) ).
fof(f595,plain,
( sK2 = sK3
| ~ s_col(sK0,sK1,sK3) ),
inference(resolution,[],[f574,f199]) ).
fof(f609,plain,
( ~ s_col(sK0,sK1,sK3)
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f595,f510]) ).
fof(f610,plain,
( $false
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f609,f300]) ).
fof(f611,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f610]) ).
cnf(s4,plain,
~ spl4_1,
inference(sat_conversion,[],[f562]) ).
cnf(s7,plain,
spl4_1,
inference(sat_conversion,[],[f611]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s4,s7]) ).
fof(f612,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO507+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 08:21:41 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 5.15/1.79 % (2682414)Detected formulas, will run a generic FOF schedule.
% 5.15/1.79 % (2682432)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=263105182:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.15/1.79 % (2682434)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=2393752881:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.15/1.79 % (2682433)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=718811441:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.15/1.79 % (2682435)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2752107828:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.15/1.79 % (2682435)Refutation not found, incomplete strategy
% 5.15/1.79 % (2682435)------------------------------
% 5.15/1.79 % (2682435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.79 % (2682435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.79 % (2682435)CaDiCaL version: 2.1.3
% 5.15/1.79 % (2682435)Termination reason: Refutation not found, incomplete strategy
% 5.15/1.79 % (2682435)Time elapsed: 0.010 s
% 5.15/1.79 % (2682435)Peak memory usage: 89 MB
% 5.15/1.79 % (2682435)Instructions burned: 8 (million)
% 5.15/1.79 % (2682437)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=327018934:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.15/1.79 % (2682436)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1091888453:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.15/1.79 % (2682438)dis-21_1_sil=8000:lcm=predicate:random_seed=2769736094: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)
% 5.15/1.79 % (2682437)First to succeed.
% 5.15/1.79 % (2682437)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2682414"
% 5.15/1.79 % (2682436)Instruction limit reached!
% 5.15/1.79 % (2682436)------------------------------
% 5.15/1.79 % (2682436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.79 % (2682436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.79 % (2682436)CaDiCaL version: 2.1.3
% 5.15/1.79 % (2682436)Termination reason: Instruction limit
% 5.15/1.79 % (2682436)Termination phase: Saturation
% 5.15/1.79 % (2682436)Time elapsed: 0.097 s
% 5.15/1.79 % (2682436)Peak memory usage: 88 MB
% 5.15/1.79 % (2682436)Instructions burned: 119 (million)
% 5.15/1.79 % (2682438)Instruction limit reached!
% 5.15/1.79 % (2682438)------------------------------
% 5.15/1.79 % (2682438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.79 % (2682438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.79 % (2682438)CaDiCaL version: 2.1.3
% 5.15/1.79 % (2682438)Termination reason: Instruction limit
% 5.15/1.79 % (2682438)Termination phase: Saturation
% 5.15/1.79 % (2682438)Time elapsed: 0.135 s
% 5.15/1.79 % (2682438)Peak memory usage: 90 MB
% 5.15/1.79 % (2682438)Instructions burned: 129 (million)
% 5.15/1.79 % (2682451)lrs+10_1_sil=8000:sp=occurrence:random_seed=1495189263:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.15/1.79 % (2682452)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2490365661:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.15/1.79 % (2682435)------------------------------
% 5.15/1.79 % (2682435)------------------------------
% 5.15/1.79 % (2682452)Refutation not found, incomplete strategy
% 5.15/1.79 % (2682452)------------------------------
% 5.15/1.79 % (2682452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.79 % (2682452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.79 % (2682452)CaDiCaL version: 2.1.3
% 5.15/1.79 % (2682452)Termination reason: Refutation not found, incomplete strategy
% 5.15/1.79 % (2682452)Time elapsed: 0.023 s
% 5.15/1.79 % (2682452)Peak memory usage: 88 MB
% 5.15/1.79 % (2682452)Instructions burned: 27 (million)
% 5.15/1.79 % (2682437)Refutation found. Thanks to Tanya!
% 5.15/1.79 % SZS status Theorem for theBenchmark
% 5.15/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 5.15/1.79 % (2682437)------------------------------
% 5.15/1.79 % (2682437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.79 % (2682437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.79 % (2682437)CaDiCaL version: 2.1.3
% 5.15/1.79 % (2682437)Termination reason: Refutation
% 5.15/1.79 % (2682437)Time elapsed: 0.021 s
% 5.15/1.79 % (2682437)Peak memory usage: 90 MB
% 5.15/1.79 % (2682437)Instructions burned: 22 (million)
% 5.15/1.79 % (2682437)------------------------------
% 5.15/1.79 % (2682437)------------------------------
% 5.15/1.79 % (2682414)Success in time 0.636 s
% 5.15/1.79 % Vampire exiting
%------------------------------------------------------------------------------