%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO454+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 : n003.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 09:52:41 AM UTC 2026
% Result : Theorem 9.69s 3.49s
% Output : Refutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2406,axiom,
s(num,i(s(fun(fun(n10,bool),num),dimindex),s(fun(n10,bool),univ))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aDIMINDEXu_1) ).
fof(f3206,axiom,
! [X0] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adrop) ).
fof(f3207,axiom,
! [X0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLIFTu_COMPONENT) ).
fof(f3209,conjecture,
! [X0] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X0))))) = s(real,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLIFTu_DROPu_conjunct1) ).
fof(f3210,negated_conjecture,
~ ! [X0] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X0))))) = s(real,X0),
inference(negated_conjecture,[status(cth)],[f3209]) ).
fof(f3219,plain,
? [X0] : s(real,X0) != s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X0))))),
inference(ennf_transformation,[],[f3210]) ).
fof(f3238,plain,
s(real,sK0) != s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,sK0))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f3219]) ).
fof(f3281,plain,
s(real,sK0) != s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,sK0))))),
inference(cnf_transformation,[],[f3238]) ).
fof(f3315,plain,
! [X0] : s(real,X0) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),
inference(cnf_transformation,[],[f3207]) ).
fof(f3316,plain,
! [X0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X0))),
inference(cnf_transformation,[],[f3206]) ).
fof(f3335,plain,
s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,i(s(fun(fun(n10,bool),num),dimindex),s(fun(n10,bool),univ))),
inference(cnf_transformation,[],[f2406]) ).
fof(f3371,plain,
! [X0] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X0))),s(num,i(s(fun(fun(n10,bool),num),dimindex),s(fun(n10,bool),univ))))),
inference(forward_demodulation,[],[f3316,f3335]) ).
fof(f3372,plain,
! [X0] : s(real,X0) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X0))))),s(num,i(s(fun(fun(n10,bool),num),dimindex),s(fun(n10,bool),univ))))),
inference(forward_demodulation,[],[f3315,f3335]) ).
fof(f3389,plain,
! [X0] : s(real,X0) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X0))))),
inference(forward_demodulation,[],[f3372,f3371]) ).
fof(f3630,plain,
s(real,sK0) != s(real,sK0),
inference(superposition,[],[f3281,f3389]) ).
fof(f3633,plain,
$false,
inference(trivial_inequality_removal,[],[f3630]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO454+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 08:16:25 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 9.69/3.49 % (192907)Detected formulas, will run a generic FOF schedule.
% 9.69/3.49 % (192913)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=431619851:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2987 on theBenchmark for (2987ds/134677Mi)
% 9.69/3.49 % (192916)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=590784658:i=119:av=off:ss=axioms_2987 on theBenchmark for (2987ds/119Mi)
% 9.69/3.49 % (192915)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3345949267:i=109:sd=1:ins=1:gsp=on:ss=axioms_2987 on theBenchmark for (2987ds/109Mi)
% 9.69/3.49 % (192912)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=2763606940:i=141193_2987 on theBenchmark for (2987ds/141193Mi)
% 9.69/3.49 % (192914)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=2091388028:i=141695:sd=1:nm=32:gsp=on:ss=included_2987 on theBenchmark for (2987ds/141695Mi)
% 9.69/3.49 % (192916)Instruction limit reached!
% 9.69/3.49 % (192916)------------------------------
% 9.69/3.49 % (192916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192916)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192916)Termination reason: Instruction limit
% 9.69/3.49 % (192916)Termination phase: Preprocessing 1
% 9.69/3.49 % (192916)Time elapsed: 0.075 s
% 9.69/3.49 % (192916)Peak memory usage: 91 MB
% 9.69/3.49 % (192916)Instructions burned: 119 (million)
% 9.69/3.49 % (192918)dis-21_1_sil=8000:lcm=predicate:random_seed=764687210:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2987 on theBenchmark for (2987ds/129Mi)
% 9.69/3.49 % (192917)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1025179416:s2a=on:i=139:gtg=position_2987 on theBenchmark for (2987ds/139Mi)
% 9.69/3.49 % (192915)Refutation not found, incomplete strategy
% 9.69/3.49 % (192915)------------------------------
% 9.69/3.49 % (192915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192915)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192915)Termination reason: Refutation not found, incomplete strategy
% 9.69/3.49 % (192915)Time elapsed: 0.074 s
% 9.69/3.49 % (192915)Peak memory usage: 94 MB
% 9.69/3.49 % (192915)Instructions burned: 87 (million)
% 9.69/3.49 % (192917)Instruction limit reached!
% 9.69/3.49 % (192917)------------------------------
% 9.69/3.49 % (192917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192917)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192917)Termination reason: Instruction limit
% 9.69/3.49 % (192917)Termination phase: Property scanning
% 9.69/3.49 % (192917)Time elapsed: 0.095 s
% 9.69/3.49 % (192917)Peak memory usage: 90 MB
% 9.69/3.49 % (192917)Instructions burned: 140 (million)
% 9.69/3.49 % (192918)Instruction limit reached!
% 9.69/3.49 % (192918)------------------------------
% 9.69/3.49 % (192918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192918)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192918)Termination reason: Instruction limit
% 9.69/3.49 % (192918)Termination phase: SInE selection
% 9.69/3.49 % (192918)Time elapsed: 0.103 s
% 9.69/3.49 % (192918)Peak memory usage: 89 MB
% 9.69/3.49 % (192918)Instructions burned: 130 (million)
% 9.69/3.49 % (192926)lrs+10_1_sil=8000:sp=occurrence:random_seed=2844452176:i=285:sd=3:ss=axioms:sgt=8_2985 on theBenchmark for (2985ds/285Mi)
% 9.69/3.49 % (192927)lrs+10_1_sil=32000:urr=on:br=off:random_seed=924585317:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/157Mi)
% 9.69/3.49 % (192927)Instruction limit reached!
% 9.69/3.49 % (192927)------------------------------
% 9.69/3.49 % (192927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192927)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192927)Termination reason: Instruction limit
% 9.69/3.49 % (192927)Termination phase: Property scanning
% 9.69/3.49 % (192927)Time elapsed: 0.062 s
% 9.69/3.49 % (192927)Peak memory usage: 90 MB
% 9.69/3.49 % (192927)Instructions burned: 158 (million)
% 9.69/3.49 % (192928)lrs+1011_1_sil=32000:sp=occurrence:random_seed=142217186:i=325:sd=1:ss=axioms:sgt=32_2984 on theBenchmark for (2984ds/325Mi)
% 9.69/3.49 % (192915)------------------------------
% 9.69/3.49 % (192915)------------------------------
% 9.69/3.49 % (192928)First to succeed.
% 9.69/3.49 % (192928)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-192907"
% 9.69/3.49 % (192926)Instruction limit reached!
% 9.69/3.49 % (192926)------------------------------
% 9.69/3.49 % (192926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192926)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192926)Termination reason: Instruction limit
% 9.69/3.49 % (192926)Termination phase: Property scanning
% 9.69/3.49 % (192926)Time elapsed: 0.234 s
% 9.69/3.49 % (192926)Peak memory usage: 96 MB
% 9.69/3.49 % (192926)Instructions burned: 286 (million)
% 9.69/3.49 % (192931)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=1786656810:s2a=on:i=248:s2at=1.23:gtg=position_2981 on theBenchmark for (2981ds/248Mi)
% 9.69/3.49 % (192933)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1453986855:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2980 on theBenchmark for (2980ds/294Mi)
% 9.69/3.49 % (192931)Instruction limit reached!
% 9.69/3.49 % (192931)------------------------------
% 9.69/3.49 % (192931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192931)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192931)Termination reason: Instruction limit
% 9.69/3.49 % (192931)Termination phase: Property scanning
% 9.69/3.49 % (192931)Time elapsed: 0.140 s
% 9.69/3.49 % (192931)Peak memory usage: 90 MB
% 9.69/3.49 % (192931)Instructions burned: 250 (million)
% 9.69/3.49 % (192934)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3328808287:i=2350_2980 on theBenchmark for (2980ds/2350Mi)
% 9.69/3.49 % (192933)Instruction limit reached!
% 9.69/3.49 % (192933)------------------------------
% 9.69/3.49 % (192933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192933)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192933)Termination reason: Instruction limit
% 9.69/3.49 % (192933)Termination phase: Property scanning
% 9.69/3.49 % (192933)Time elapsed: 0.136 s
% 9.69/3.49 % (192933)Peak memory usage: 95 MB
% 9.69/3.49 % (192933)Instructions burned: 296 (million)
% 9.69/3.49 % (192928)Refutation found. Thanks to Tanya!
% 9.69/3.49 % SZS status Theorem for theBenchmark
% 9.69/3.49 % SZS output start Proof for theBenchmark
% See solution above
% 9.69/3.49 % (192928)------------------------------
% 9.69/3.49 % (192928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.69/3.49 % (192928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.69/3.49 % (192928)CaDiCaL version: 2.1.3
% 9.69/3.49 % (192928)Termination reason: Refutation
% 9.69/3.49 % (192928)Time elapsed: 0.086 s
% 9.69/3.49 % (192928)Peak memory usage: 95 MB
% 9.69/3.49 % (192928)Instructions burned: 98 (million)
% 9.69/3.49 % (192928)------------------------------
% 9.69/3.49 % (192928)------------------------------
% 9.69/3.49 % (192907)Success in time 2.334 s
% 9.69/3.49 % Vampire exiting
%------------------------------------------------------------------------------