%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO025-3 : 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 : 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 09:51:14 AM UTC 2026
% Result : Unsatisfiable 5.37s 1.72s
% Output : Refutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 25 ( 19 unt; 0 def)
% Number of atoms : 39 ( 4 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( equidistant(X4,X6,X5,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X6,X3,X7)
| ~ between(X0,X1,X4)
| ~ between(X2,X3,X5)
| X0 = X1
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f20,axiom,
! [X0,X1] : equidistant(X0,X1,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( equidistant(X0,X1,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
fof(f28,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
fof(f41,axiom,
! [X0,X1] : equidistant(X0,X0,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
fof(f42,axiom,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
fof(f43,axiom,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
fof(f44,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f45,axiom,
between(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
fof(f46,negated_conjecture,
~ equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_sums) ).
fof(f64,plain,
~ equidistant(u,w,w1,u1),
inference(unit_resulting_resolution,[],[f23,f46]) ).
fof(f65,plain,
~ equidistant(w,u,w1,u1),
inference(unit_resulting_resolution,[],[f24,f46]) ).
fof(f127,plain,
equidistant(u1,v1,u,v),
inference(unit_resulting_resolution,[],[f2,f20,f42]) ).
fof(f134,plain,
equidistant(v,u,v1,u1),
inference(unit_resulting_resolution,[],[f24,f42]) ).
fof(f476,plain,
u = v,
inference(unit_resulting_resolution,[],[f6,f44,f45,f42,f41,f65,f43,f134]) ).
fof(f492,plain,
equidistant(u,w,v1,w1),
inference(backward_demodulation,[],[f43,f476]) ).
fof(f496,plain,
equidistant(u1,v1,u,u),
inference(backward_demodulation,[],[f127,f476]) ).
fof(f572,plain,
~ equidistant(v1,w1,w1,u1),
inference(unit_resulting_resolution,[],[f28,f64,f492]) ).
fof(f600,plain,
u1 = v1,
inference(unit_resulting_resolution,[],[f3,f496]) ).
fof(f620,plain,
~ equidistant(u1,w1,w1,u1),
inference(backward_demodulation,[],[f572,f600]) ).
fof(f623,plain,
$false,
inference(forward_subsumption_resolution,[],[f620,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO025-3 : 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 : n002.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 06:38:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 5.37/1.72 % (3180907)Input is clausal, will run a generic CNF schedule.
% 5.37/1.72 % (3180915)lrs+10_1_sil=8000:sp=occurrence:random_seed=1091851297:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.37/1.72 % (3180915)Refutation not found, incomplete strategy
% 5.37/1.72 % (3180915)------------------------------
% 5.37/1.72 % (3180915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180915)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180915)Termination reason: Refutation not found, incomplete strategy
% 5.37/1.72 % (3180915)Time elapsed: 0.002 s
% 5.37/1.72 % (3180915)Peak memory usage: 87 MB
% 5.37/1.72 % (3180915)Instructions burned: 5 (million)
% 5.37/1.72 % (3180918)dis-21_1_sil=8000:lcm=predicate:random_seed=3900967129: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)
% 5.37/1.72 % (3180913)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=273212736:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.37/1.72 % (3180914)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2394352963:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.37/1.72 % (3180912)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=4030921919:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.37/1.72 % (3180916)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2164664894:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.37/1.72 % (3180917)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2342426636:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.37/1.72 % (3180918)Instruction limit reached!
% 5.37/1.72 % (3180918)------------------------------
% 5.37/1.72 % (3180918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180918)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180918)Termination reason: Instruction limit
% 5.37/1.72 % (3180918)Termination phase: Saturation
% 5.37/1.72 % (3180918)Time elapsed: 0.062 s
% 5.37/1.72 % (3180918)Peak memory usage: 88 MB
% 5.37/1.72 % (3180918)Instructions burned: 117 (million)
% 5.37/1.72 % (3180916)Instruction limit reached!
% 5.37/1.72 % (3180916)------------------------------
% 5.37/1.72 % (3180916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180916)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180916)Termination reason: Instruction limit
% 5.37/1.72 % (3180916)Termination phase: Saturation
% 5.37/1.72 % (3180916)Time elapsed: 0.063 s
% 5.37/1.72 % (3180916)Peak memory usage: 88 MB
% 5.37/1.72 % (3180916)Instructions burned: 115 (million)
% 5.37/1.72 % (3180917)Instruction limit reached!
% 5.37/1.72 % (3180917)------------------------------
% 5.37/1.72 % (3180917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180917)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180917)Termination reason: Instruction limit
% 5.37/1.72 % (3180917)Termination phase: Saturation
% 5.37/1.72 % (3180917)Time elapsed: 0.101 s
% 5.37/1.72 % (3180917)Peak memory usage: 89 MB
% 5.37/1.72 % (3180917)Instructions burned: 181 (million)
% 5.37/1.72 % (3180915)------------------------------
% 5.37/1.72 % (3180915)------------------------------
% 5.37/1.72 % (3180926)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2849097292:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.37/1.72 % (3180927)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3005171081:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.37/1.72 % (3180926)Refutation not found, incomplete strategy
% 5.37/1.72 % (3180926)------------------------------
% 5.37/1.72 % (3180926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180926)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180926)Termination reason: Refutation not found, incomplete strategy
% 5.37/1.72 % (3180926)Time elapsed: 0.004 s
% 5.37/1.72 % (3180926)Peak memory usage: 87 MB
% 5.37/1.72 % (3180926)Instructions burned: 5 (million)
% 5.37/1.72 % (3180928)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2483674881:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.37/1.72 % (3180927)First to succeed.
% 5.37/1.72 % (3180927)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3180907"
% 5.37/1.72 % (3180929)lrs+10_64_to=lpo:sil=8000:random_seed=4241527202:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.37/1.72 % (3180929)Instruction limit reached!
% 5.37/1.72 % (3180929)------------------------------
% 5.37/1.72 % (3180929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180929)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180929)Termination reason: Instruction limit
% 5.37/1.72 % (3180929)Termination phase: Saturation
% 5.37/1.72 % (3180929)Time elapsed: 0.042 s
% 5.37/1.72 % (3180929)Peak memory usage: 89 MB
% 5.37/1.72 % (3180929)Instructions burned: 128 (million)
% 5.37/1.72 % (3180928)Instruction limit reached!
% 5.37/1.72 % (3180928)------------------------------
% 5.37/1.72 % (3180928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180928)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180928)Termination reason: Instruction limit
% 5.37/1.72 % (3180928)Termination phase: Saturation
% 5.37/1.72 % (3180928)Time elapsed: 0.128 s
% 5.37/1.72 % (3180928)Peak memory usage: 89 MB
% 5.37/1.72 % (3180928)Instructions burned: 219 (million)
% 5.37/1.72 % (3180934)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=998537584:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.37/1.72 % (3180926)------------------------------
% 5.37/1.72 % (3180926)------------------------------
% 5.37/1.72 % (3180934)Instruction limit reached!
% 5.37/1.72 % (3180934)------------------------------
% 5.37/1.72 % (3180934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180934)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180934)Termination reason: Instruction limit
% 5.37/1.72 % (3180934)Termination phase: Saturation
% 5.37/1.72 % (3180934)Time elapsed: 0.061 s
% 5.37/1.72 % (3180934)Peak memory usage: 89 MB
% 5.37/1.72 % (3180934)Instructions burned: 196 (million)
% 5.37/1.72 % (3180927)Refutation found. Thanks to Tanya!
% 5.37/1.72 % SZS status Unsatisfiable for theBenchmark
% 5.37/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 5.37/1.72 % (3180927)------------------------------
% 5.37/1.72 % (3180927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.72 % (3180927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.72 % (3180927)CaDiCaL version: 2.1.3
% 5.37/1.72 % (3180927)Termination reason: Refutation
% 5.37/1.72 % (3180927)Time elapsed: 0.033 s
% 5.37/1.72 % (3180927)Peak memory usage: 88 MB
% 5.37/1.72 % (3180927)Instructions burned: 61 (million)
% 5.37/1.72 % (3180927)------------------------------
% 5.37/1.72 % (3180927)------------------------------
% 5.37/1.72 % (3180907)Success in time 0.672 s
% 5.37/1.72 % Vampire exiting
%------------------------------------------------------------------------------