%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO531+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:52:52 AM UTC 2026
% Result : Theorem 4.32s 1.59s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 101 ( 46 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 112 ( 31 ~; 68 |; 13 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-6 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-6 aty)
% Number of variables : 63 ( 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] : s_e(X0,X1,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_1) ).
fof(f203,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sameside(X0,X1,X2)
| ~ sameside(X3,X1,X4)
| ~ sameside(X5,X6,X7)
| ~ sameside(X8,X6,X9)
| ~ s_e3(X0,X1,X3,X5,X6,X8)
| congruent(X2,X1,X4,X7,X6,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_3d) ).
fof(f204,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( X0 = X1
| X2 = X1
| X3 = X4
| X5 = X4
| sameside(f113a(X0,X1,X2,X3,X4,X5),X1,X0)
| congruent(X0,X1,X2,X3,X4,X5) )
& ( X0 = X1
| X2 = X1
| X3 = X4
| X5 = X4
| sameside(f113c(X0,X1,X2,X3,X4,X5),X1,X2)
| congruent(X0,X1,X2,X3,X4,X5) )
& ( X0 = X1
| X2 = X1
| X3 = X4
| X5 = X4
| sameside(f113d(X0,X1,X2,X3,X4,X5),X4,X3)
| congruent(X0,X1,X2,X3,X4,X5) )
& ( X0 = X1
| X2 = X1
| X3 = X4
| X5 = X4
| sameside(f113f(X0,X1,X2,X3,X4,X5),X4,X5)
| congruent(X0,X1,X2,X3,X4,X5) )
& ( X0 = X1
| X2 = X1
| X3 = X4
| X5 = X4
| s_e(X1,f113a(X0,X1,X2,X3,X4,X5),X4,f113d(X0,X1,X2,X3,X4,X5))
| congruent(X0,X1,X2,X3,X4,X5) )
& ( X0 = X1
| X2 = X1
| X3 = X4
| X5 = X4
| s_e(X1,f113c(X0,X1,X2,X3,X4,X5),X4,f113f(X0,X1,X2,X3,X4,X5))
| congruent(X0,X1,X2,X3,X4,X5) )
& ( X0 = X1
| X2 = X1
| X3 = X4
| X5 = X4
| ~ s_e(f113a(X0,X1,X2,X3,X4,X5),f113c(X0,X1,X2,X3,X4,X5),f113d(X0,X1,X2,X3,X4,X5),f113f(X0,X1,X2,X3,X4,X5))
| congruent(X0,X1,X2,X3,X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_4b) ).
fof(f207,conjecture,
! [X0,X1,X2] :
( X0 = X1
| X2 = X1
| congruent(X0,X1,X2,X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz11_6) ).
fof(f208,negated_conjecture,
~ ! [X0,X1,X2] :
( X0 = X1
| X2 = X1
| congruent(X0,X1,X2,X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f207]) ).
fof(f212,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ~ s_e3(X0,X1,X2,X3,X4,X5)
| s_e(X0,X1,X3,X4) )
& ( ~ s_e3(X0,X1,X2,X3,X4,X5)
| s_e(X0,X2,X3,X5) )
& ( ~ s_e3(X0,X1,X2,X3,X4,X5)
| s_e(X1,X2,X4,X5) )
& ( ~ s_e(X0,X1,X3,X4)
| ~ s_e(X0,X2,X3,X5)
| ~ s_e(X1,X2,X4,X5)
| s_e3(X0,X1,X2,X3,X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn4_4) ).
fof(f224,plain,
? [X0,X1,X2] :
( X0 != X1
& X1 != X2
& ~ congruent(X0,X1,X2,X0,X1,X2) ),
inference(ennf_transformation,[],[f208]) ).
fof(f225,plain,
( sK0 != sK1
& sK1 != sK2
& ~ congruent(sK0,sK1,sK2,sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f224]) ).
fof(f238,plain,
! [X0,X1] : s_e(X0,X1,X0,X1),
inference(cnf_transformation,[],[f9]) ).
fof(f465,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ s_e3(X0,X1,X3,X5,X6,X8)
| ~ sameside(X3,X1,X4)
| ~ sameside(X5,X6,X7)
| ~ sameside(X8,X6,X9)
| ~ sameside(X0,X1,X2)
| congruent(X2,X1,X4,X7,X6,X9) ),
inference(cnf_transformation,[],[f203]) ).
fof(f469,plain,
! [X2,X3,X0,X1,X4,X5] :
( sameside(f113f(X0,X1,X2,X3,X4,X5),X4,X5)
| X1 = X2
| X3 = X4
| X4 = X5
| X0 = X1
| congruent(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f204]) ).
fof(f470,plain,
! [X2,X3,X0,X1,X4,X5] :
( sameside(f113d(X0,X1,X2,X3,X4,X5),X4,X3)
| X1 = X2
| X3 = X4
| X4 = X5
| X0 = X1
| congruent(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f204]) ).
fof(f475,plain,
~ congruent(sK0,sK1,sK2,sK0,sK1,sK2),
inference(cnf_transformation,[],[f225]) ).
fof(f476,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f225]) ).
fof(f477,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f225]) ).
fof(f493,plain,
! [X2,X3,X0,X1,X4,X5] :
( s_e3(X0,X1,X2,X3,X4,X5)
| ~ s_e(X0,X2,X3,X5)
| ~ s_e(X1,X2,X4,X5)
| ~ s_e(X0,X1,X3,X4) ),
inference(cnf_transformation,[],[f212]) ).
fof(f578,plain,
sameside(f113f(sK0,sK1,sK2,sK0,sK1,sK2),sK1,sK2),
inference(unit_resulting_resolution,[],[f469,f477,f477,f476,f475,f476]) ).
fof(f579,plain,
sameside(f113d(sK0,sK1,sK2,sK0,sK1,sK2),sK1,sK0),
inference(unit_resulting_resolution,[],[f470,f477,f477,f476,f475,f476]) ).
fof(f582,plain,
~ s_e3(f113d(sK0,sK1,sK2,sK0,sK1,sK2),sK1,f113f(sK0,sK1,sK2,sK0,sK1,sK2),f113d(sK0,sK1,sK2,sK0,sK1,sK2),sK1,f113f(sK0,sK1,sK2,sK0,sK1,sK2)),
inference(unit_resulting_resolution,[],[f465,f579,f579,f578,f475,f578]) ).
fof(f1036,plain,
$false,
inference(unit_resulting_resolution,[],[f493,f238,f238,f238,f582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO531+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 08:30:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 4.32/1.59 % (1347133)Detected formulas, will run a generic FOF schedule.
% 4.32/1.59 % (1347141)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1026239617:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.32/1.59 % (1347141)Refutation not found, incomplete strategy
% 4.32/1.59 % (1347141)------------------------------
% 4.32/1.59 % (1347141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1347141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1347141)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1347141)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.59 % (1347141)Time elapsed: 0.002 s
% 4.32/1.59 % (1347141)Peak memory usage: 88 MB
% 4.32/1.59 % (1347141)Instructions burned: 2 (million)
% 4.32/1.59 % (1347142)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2078883110:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.32/1.59 % (1347140)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=3276962958:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.32/1.59 % (1347139)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=2443927489:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.32/1.59 % (1347138)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=1415867944:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.32/1.59 % (1347144)dis-21_1_sil=8000:lcm=predicate:random_seed=1201678838: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)
% 4.32/1.59 % (1347143)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1601308068:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.32/1.59 % (1347142)Instruction limit reached!
% 4.32/1.59 % (1347142)------------------------------
% 4.32/1.59 % (1347142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1347142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1347142)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1347142)Termination reason: Instruction limit
% 4.32/1.59 % (1347142)Termination phase: Saturation
% 4.32/1.59 % (1347142)Time elapsed: 0.070 s
% 4.32/1.59 % (1347142)Peak memory usage: 88 MB
% 4.32/1.59 % (1347142)Instructions burned: 121 (million)
% 4.32/1.59 % (1347144)Instruction limit reached!
% 4.32/1.59 % (1347144)------------------------------
% 4.32/1.59 % (1347144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1347144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1347144)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1347144)Termination reason: Instruction limit
% 4.32/1.59 % (1347144)Termination phase: Saturation
% 4.32/1.59 % (1347144)Time elapsed: 0.073 s
% 4.32/1.59 % (1347144)Peak memory usage: 89 MB
% 4.32/1.59 % (1347144)Instructions burned: 130 (million)
% 4.32/1.59 % (1347143)Instruction limit reached!
% 4.32/1.59 % (1347143)------------------------------
% 4.32/1.59 % (1347143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1347143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1347143)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1347143)Termination reason: Instruction limit
% 4.32/1.59 % (1347143)Termination phase: Saturation
% 4.32/1.59 % (1347143)Time elapsed: 0.092 s
% 4.32/1.59 % (1347143)Peak memory usage: 90 MB
% 4.32/1.59 % (1347143)Instructions burned: 139 (million)
% 4.32/1.59 % (1347141)------------------------------
% 4.32/1.59 % (1347141)------------------------------
% 4.32/1.59 % (1347152)lrs+10_1_sil=8000:sp=occurrence:random_seed=2306180052:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.32/1.59 % (1347155)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3212797102:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.32/1.59 % (1347155)First to succeed.
% 4.32/1.59 % (1347155)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1347133"
% 4.32/1.59 % (1347153)lrs+10_1_sil=32000:urr=on:br=off:random_seed=136790255:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.32/1.59 % (1347153)Refutation not found, incomplete strategy
% 4.32/1.59 % (1347153)------------------------------
% 4.32/1.59 % (1347153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1347153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1347153)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1347153)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.59 % (1347153)Time elapsed: 0.006 s
% 4.32/1.59 % (1347153)Peak memory usage: 89 MB
% 4.32/1.59 % (1347153)Instructions burned: 9 (million)
% 4.32/1.59 % (1347154)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2948421006:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.32/1.59 % (1347154)Refutation not found, incomplete strategy
% 4.32/1.59 % (1347154)------------------------------
% 4.32/1.59 % (1347154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1347154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1347154)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1347154)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.59 % (1347154)Time elapsed: 0.003 s
% 4.32/1.59 % (1347154)Peak memory usage: 88 MB
% 4.32/1.59 % (1347154)Instructions burned: 3 (million)
% 4.32/1.59 % (1347155)Refutation found. Thanks to Tanya!
% 4.32/1.59 % SZS status Theorem for theBenchmark
% 4.32/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 4.32/1.59 % (1347155)------------------------------
% 4.32/1.59 % (1347155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.59 % (1347155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.59 % (1347155)CaDiCaL version: 2.1.3
% 4.32/1.59 % (1347155)Termination reason: Refutation
% 4.32/1.59 % (1347155)Time elapsed: 0.014 s
% 4.32/1.59 % (1347155)Peak memory usage: 89 MB
% 4.32/1.59 % (1347155)Instructions burned: 45 (million)
% 4.32/1.59 % (1347155)------------------------------
% 4.32/1.59 % (1347155)------------------------------
% 4.32/1.59 % (1347133)Success in time 0.538 s
% 4.32/1.59 % Vampire exiting
%------------------------------------------------------------------------------