%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO474+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 : n010.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 09:52:45 AM UTC 2026
% Result : Theorem 10.25s 3.82s
% Output : Refutation 10.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 12 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 21 ( 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f200,axiom,
! [X0] : s(num,i(s(fun(num,num),numeral),s(num,X0))) = s(num,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aNUMERAL) ).
fof(f3502,axiom,
! [X0,X1,X2] :
( s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),X2))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))
<=> s(cart(cart(real,X0),X1),X2) = s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aRANKu_EQu_0) ).
fof(f3503,conjecture,
! [X0,X1] : s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aRANKu_0) ).
fof(f3504,negated_conjecture,
~ ! [X0,X1] : s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))),
inference(negated_conjecture,[status(cth)],[f3503]) ).
fof(f3510,plain,
? [X0,X1] : s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
inference(ennf_transformation,[],[f3504]) ).
fof(f3526,plain,
s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(cart(cart(real,sK0),sK1),num),rank),s(cart(cart(real,sK0),sK1),i(s(fun(num,cart(cart(real,sK0),sK1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3510]) ).
fof(f3550,plain,
! [X0,X1,X2] :
( ( s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),X2))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))
| s(cart(cart(real,X0),X1),X2) != s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
& ( s(cart(cart(real,X0),X1),X2) = s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),X2))) ) ),
inference(nnf_transformation,[],[f3502]) ).
fof(f3564,plain,
s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(cart(cart(real,sK0),sK1),num),rank),s(cart(cart(real,sK0),sK1),i(s(fun(num,cart(cart(real,sK0),sK1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
inference(cnf_transformation,[],[f3526]) ).
fof(f3600,plain,
! [X0] : s(num,X0) = s(num,i(s(fun(num,num),numeral),s(num,X0))),
inference(cnf_transformation,[],[f200]) ).
fof(f3607,plain,
! [X2,X0,X1] :
( s(cart(cart(real,X0),X1),X2) != s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),X2))) ),
inference(cnf_transformation,[],[f3550]) ).
fof(f3626,plain,
s(num,u_0) != s(num,i(s(fun(cart(cart(real,sK0),sK1),num),rank),s(cart(cart(real,sK0),sK1),i(s(fun(num,cart(cart(real,sK0),sK1)),mat),s(num,u_0))))),
inference(forward_demodulation,[],[f3564,f3600]) ).
fof(f3743,plain,
! [X0,X1] : s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
inference(equality_resolution,[],[f3607]) ).
fof(f3744,plain,
! [X0,X1] : s(num,u_0) = s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,u_0))))),
inference(forward_demodulation,[],[f3743,f3600]) ).
fof(f3745,plain,
s(num,u_0) != s(num,u_0),
inference(superposition,[],[f3626,f3744]) ).
fof(f3756,plain,
$false,
inference(trivial_inequality_removal,[],[f3745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO474+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n010.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 08:20:01 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 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
% 10.25/3.81 % (634521)Detected formulas, will run a generic FOF schedule.
% 10.25/3.81 % (634526)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=376973309:i=141193_2986 on theBenchmark for (2986ds/141193Mi)
% 10.25/3.81 % (634531)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2039171595:s2a=on:i=139:gtg=position_2986 on theBenchmark for (2986ds/139Mi)
% 10.25/3.81 % (634530)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3870699477:i=119:av=off:ss=axioms_2986 on theBenchmark for (2986ds/119Mi)
% 10.25/3.81 % (634528)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=93865668:i=141695:sd=1:nm=32:gsp=on:ss=included_2986 on theBenchmark for (2986ds/141695Mi)
% 10.25/3.81 % (634532)dis-21_1_sil=8000:lcm=predicate:random_seed=2268338410:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2986 on theBenchmark for (2986ds/129Mi)
% 10.25/3.81 % (634529)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1208307853:i=109:sd=1:ins=1:gsp=on:ss=axioms_2986 on theBenchmark for (2986ds/109Mi)
% 10.25/3.81 % (634527)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=4014382836:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2986 on theBenchmark for (2986ds/134677Mi)
% 10.25/3.81 % (634531)Instruction limit reached!
% 10.25/3.81 % (634531)------------------------------
% 10.25/3.81 % (634531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/3.81 % (634531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/3.81 % (634531)CaDiCaL version: 2.1.3
% 10.25/3.81 % (634531)Termination reason: Instruction limit
% 10.25/3.81 % (634531)Termination phase: Property scanning
% 10.25/3.81 % (634531)Time elapsed: 0.087 s
% 10.25/3.81 % (634531)Peak memory usage: 90 MB
% 10.25/3.81 % (634531)Instructions burned: 140 (million)
% 10.25/3.81 % (634529)Refutation not found, incomplete strategy
% 10.25/3.81 % (634529)------------------------------
% 10.25/3.81 % (634529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/3.81 % (634529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/3.81 % (634529)CaDiCaL version: 2.1.3
% 10.25/3.81 % (634529)Termination reason: Refutation not found, incomplete strategy
% 10.25/3.81 % (634529)Time elapsed: 0.086 s
% 10.25/3.81 % (634529)Peak memory usage: 94 MB
% 10.25/3.81 % (634529)Instructions burned: 101 (million)
% 10.25/3.81 % (634532)Instruction limit reached!
% 10.25/3.81 % (634532)------------------------------
% 10.25/3.81 % (634532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/3.81 % (634532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/3.81 % (634532)CaDiCaL version: 2.1.3
% 10.25/3.81 % (634532)Termination reason: Instruction limit
% 10.25/3.81 % (634532)Termination phase: SInE selection
% 10.25/3.81 % (634532)Time elapsed: 0.099 s
% 10.25/3.81 % (634532)Peak memory usage: 90 MB
% 10.25/3.81 % (634532)Instructions burned: 130 (million)
% 10.25/3.81 % (634530)Instruction limit reached!
% 10.25/3.81 % (634530)------------------------------
% 10.25/3.81 % (634530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/3.81 % (634530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/3.81 % (634530)CaDiCaL version: 2.1.3
% 10.25/3.81 % (634530)Termination reason: Instruction limit
% 10.25/3.81 % (634530)Termination phase: Preprocessing 1
% 10.25/3.81 % (634530)Time elapsed: 0.101 s
% 10.25/3.81 % (634530)Peak memory usage: 91 MB
% 10.25/3.81 % (634530)Instructions burned: 119 (million)
% 10.25/3.81 % (634542)lrs+10_1_sil=8000:sp=occurrence:random_seed=936689226:i=285:sd=3:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/285Mi)
% 10.25/3.81 % (634544)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3394526645:i=325:sd=1:ss=axioms:sgt=32_2982 on theBenchmark for (2982ds/325Mi)
% 10.25/3.81 % (634543)lrs+10_1_sil=32000:urr=on:br=off:random_seed=803272394:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2982 on theBenchmark for (2982ds/157Mi)
% 10.25/3.81 % (634544)First to succeed.
% 10.25/3.81 % (634544)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-634521"
% 10.25/3.81 % (634529)------------------------------
% 10.25/3.81 % (634529)------------------------------
% 10.25/3.81 % (634543)Instruction limit reached!
% 10.25/3.81 % (634543)------------------------------
% 10.25/3.81 % (634543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/3.81 % (634543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/3.81 % (634543)CaDiCaL version: 2.1.3
% 10.25/3.81 % (634543)Termination reason: Instruction limit
% 10.25/3.81 % (634543)Termination phase: Property scanning
% 10.25/3.81 % (634543)Time elapsed: 0.121 s
% 10.25/3.81 % (634543)Peak memory usage: 90 MB
% 10.25/3.81 % (634543)Instructions burned: 157 (million)
% 10.25/3.81 % (634542)Instruction limit reached!
% 10.25/3.81 % (634542)------------------------------
% 10.25/3.81 % (634542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/3.81 % (634542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/3.81 % (634542)CaDiCaL version: 2.1.3
% 10.25/3.81 % (634542)Termination reason: Instruction limit
% 10.25/3.81 % (634542)Termination phase: Property scanning
% 10.25/3.81 % (634542)Time elapsed: 0.230 s
% 10.25/3.81 % (634542)Peak memory usage: 95 MB
% 10.25/3.81 % (634542)Instructions burned: 285 (million)
% 10.25/3.81 % (634549)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=182221425:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2978 on theBenchmark for (2978ds/294Mi)
% 10.25/3.82 % (634548)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=611075273:s2a=on:i=248:s2at=1.23:gtg=position_2978 on theBenchmark for (2978ds/248Mi)
% 10.25/3.82 % (634550)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1776826989:i=2350_2978 on theBenchmark for (2978ds/2350Mi)
% 10.25/3.82 % (634544)Refutation found. Thanks to Tanya!
% 10.25/3.82 % SZS status Theorem for theBenchmark
% 10.25/3.82 % SZS output start Proof for theBenchmark
% See solution above
% 10.25/3.82 % (634544)------------------------------
% 10.25/3.82 % (634544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/3.82 % (634544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/3.82 % (634544)CaDiCaL version: 2.1.3
% 10.25/3.82 % (634544)Termination reason: Refutation
% 10.25/3.82 % (634544)Time elapsed: 0.104 s
% 10.25/3.82 % (634544)Peak memory usage: 95 MB
% 10.25/3.82 % (634544)Instructions burned: 114 (million)
% 10.25/3.82 % (634544)------------------------------
% 10.25/3.82 % (634544)------------------------------
% 10.25/3.82 % (634521)Success in time 2.49 s
% 10.25/3.82 % Vampire exiting
%------------------------------------------------------------------------------