%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 10:13:18 AM UTC 2026
% Result : Theorem 5.28s 1.94s
% Output : Refutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 125 ( 26 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 150 ( 66 ~; 60 |; 18 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 61 ( 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( group_member(X0,f)
=> group_member(phi(X0),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f4,axiom,
! [X0,X1] :
( ( group_member(X0,f)
& group_member(X1,f) )
=> multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f5,axiom,
! [X0] :
( group_member(X0,h)
=> ? [X1] :
( group_member(X1,f)
& phi(X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f6,axiom,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( group_member(X1,X0)
& ! [X2] :
( group_member(X2,X0)
=> multiply(X0,X1,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
fof(f7,axiom,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
fof(f8,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
fof(f9,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
~ left_zero(h,phi(f_left_zero)),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ? [X1] :
( group_member(X1,f)
& phi(X1) = X0 )
| ~ group_member(X0,h) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X0,f)
| ~ group_member(X1,f) ),
inference(ennf_transformation,[],[f4]) ).
fof(f13,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X0,f)
| ~ group_member(X1,f) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( group_member(X1,X0)
& ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0] :
( ( group_member(sK0(X0),f)
& phi(sK0(X0)) = X0 )
| ~ group_member(X0,h) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f11]) ).
fof(f21,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ~ group_member(X1,X0)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) ) )
& ( ( group_member(X1,X0)
& ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) ) )
| ~ left_zero(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ~ group_member(X1,X0)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) ) )
& ( ( group_member(X1,X0)
& ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) ) )
| ~ left_zero(X0,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ~ group_member(X1,X0)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) ) )
& ( ( group_member(X1,X0)
& ! [X3] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0) ) )
| ~ left_zero(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ~ group_member(X1,X0)
| ( multiply(X0,X1,sK1(X0,X1)) != X1
& group_member(sK1(X0,X1),X0) ) )
& ( ( group_member(X1,X0)
& ! [X3] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0) ) )
| ~ left_zero(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f23]) ).
fof(f25,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[],[f10]) ).
fof(f27,plain,
! [X0] :
( phi(sK0(X0)) = X0
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0] :
( group_member(sK0(X0),f)
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X0,f)
| ~ group_member(X1,f) ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X3,X0,X1] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X0,X1] :
( group_member(X1,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X0,X1] :
( group_member(sK1(X0,X1),X0)
| ~ group_member(X1,X0)
| left_zero(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X0,X1] :
( multiply(X0,X1,sK1(X0,X1)) != X1
| ~ group_member(X1,X0)
| left_zero(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
! [X0,X1] :
( phi(multiply(f,X1,sK0(X0))) = multiply(h,phi(X1),X0)
| ~ group_member(X1,f)
| ~ group_member(sK0(X0),f)
| ~ group_member(X0,h) ),
inference(superposition,[],[f29,f27]) ).
fof(f49,plain,
! [X0,X1] :
( phi(multiply(f,X1,sK0(X0))) = multiply(h,phi(X1),X0)
| ~ group_member(X1,f)
| ~ group_member(X0,h) ),
inference(forward_subsumption_resolution,[],[f42,f28]) ).
fof(f85,plain,
! [X0,X1] :
( phi(X0) = multiply(h,phi(X0),X1)
| ~ group_member(X0,f)
| ~ group_member(X1,h)
| ~ group_member(sK0(X1),f)
| ~ left_zero(f,X0) ),
inference(superposition,[],[f49,f31]) ).
fof(f98,plain,
! [X0,X1] :
( phi(X0) = multiply(h,phi(X0),X1)
| ~ group_member(X1,h)
| ~ group_member(sK0(X1),f)
| ~ left_zero(f,X0) ),
inference(forward_subsumption_resolution,[],[f85,f32]) ).
fof(f100,plain,
! [X0,X1] :
( phi(X0) = multiply(h,phi(X0),X1)
| ~ group_member(X1,h)
| ~ left_zero(f,X0) ),
inference(forward_subsumption_resolution,[],[f98,f28]) ).
fof(f165,plain,
! [X0] :
( phi(X0) != phi(X0)
| ~ group_member(phi(X0),h)
| left_zero(h,phi(X0))
| ~ group_member(sK1(h,phi(X0)),h)
| ~ left_zero(f,X0) ),
inference(superposition,[],[f34,f100]) ).
fof(f167,plain,
! [X0] :
( ~ group_member(phi(X0),h)
| left_zero(h,phi(X0))
| ~ group_member(sK1(h,phi(X0)),h)
| ~ left_zero(f,X0) ),
inference(trivial_inequality_removal,[],[f165]) ).
fof(f172,plain,
! [X0] :
( left_zero(h,phi(X0))
| ~ group_member(phi(X0),h)
| ~ left_zero(f,X0) ),
inference(forward_subsumption_resolution,[],[f167,f33]) ).
fof(f215,plain,
( ~ group_member(phi(f_left_zero),h)
| ~ left_zero(f,f_left_zero) ),
inference(resolution,[],[f172,f26]) ).
fof(f223,plain,
~ group_member(phi(f_left_zero),h),
inference(forward_subsumption_resolution,[],[f215,f25]) ).
fof(f270,plain,
~ group_member(f_left_zero,f),
inference(resolution,[],[f223,f30]) ).
fof(f272,plain,
~ left_zero(f,f_left_zero),
inference(resolution,[],[f270,f32]) ).
fof(f273,plain,
$false,
inference(forward_subsumption_resolution,[],[f272,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 09:43:01 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 5.28/1.94 % (3304036)Detected formulas, will run a generic FOF schedule.
% 5.28/1.94 % (3304053)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=554399443:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.28/1.94 % (3304051)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=1204355780:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.28/1.94 % (3304055)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2526732017:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.28/1.94 % (3304055)First to succeed.
% 5.28/1.94 % (3304055)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3304036"
% 5.28/1.94 % (3304054)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2906463575:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.28/1.94 % (3304052)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=4073762857:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.28/1.94 % (3304054)Refutation not found, incomplete strategy
% 5.28/1.94 % (3304054)------------------------------
% 5.28/1.94 % (3304054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.94 % (3304054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.94 % (3304054)CaDiCaL version: 2.1.3
% 5.28/1.94 % (3304054)Termination reason: Refutation not found, incomplete strategy
% 5.28/1.94 % (3304054)Time elapsed: 0.002 s
% 5.28/1.94 % (3304054)Peak memory usage: 88 MB
% 5.28/1.94 % (3304056)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4093990190:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.28/1.94 % (3304057)dis-21_1_sil=8000:lcm=predicate:random_seed=96270161: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)
% 5.28/1.94 % (3304057)Refutation not found, incomplete strategy
% 5.28/1.94 % (3304057)------------------------------
% 5.28/1.94 % (3304057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.94 % (3304057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.94 % (3304057)CaDiCaL version: 2.1.3
% 5.28/1.94 % (3304057)Termination reason: Refutation not found, incomplete strategy
% 5.28/1.94 % (3304057)Time elapsed: 0.003 s
% 5.28/1.94 % (3304057)Peak memory usage: 88 MB
% 5.28/1.94 % (3304057)Instructions burned: 1 (million)
% 5.28/1.94 % (3304056)Instruction limit reached!
% 5.28/1.94 % (3304056)------------------------------
% 5.28/1.94 % (3304056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.94 % (3304056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.94 % (3304056)CaDiCaL version: 2.1.3
% 5.28/1.94 % (3304056)Termination reason: Instruction limit
% 5.28/1.94 % (3304056)Termination phase: Saturation
% 5.28/1.94 % (3304056)Time elapsed: 0.142 s
% 5.28/1.94 % (3304056)Peak memory usage: 89 MB
% 5.28/1.94 % (3304056)Instructions burned: 139 (million)
% 5.28/1.94 % (3304065)lrs+10_1_sil=8000:sp=occurrence:random_seed=3927482424:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.28/1.94 % (3304065)Also succeeded, but the first one will report.
% 5.28/1.94 % (3304054)------------------------------
% 5.28/1.94 % (3304054)------------------------------
% 5.28/1.94 % (3304055)Refutation found. Thanks to Tanya!
% 5.28/1.94 % SZS status Theorem for theBenchmark
% 5.28/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 5.28/1.94 % (3304055)------------------------------
% 5.28/1.94 % (3304055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.94 % (3304055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.94 % (3304055)CaDiCaL version: 2.1.3
% 5.28/1.94 % (3304055)Termination reason: Refutation
% 5.28/1.94 % (3304055)Time elapsed: 0.012 s
% 5.28/1.94 % (3304055)Peak memory usage: 88 MB
% 5.28/1.94 % (3304055)Instructions burned: 10 (million)
% 5.28/1.94 % (3304055)------------------------------
% 5.28/1.94 % (3304055)------------------------------
% 5.28/1.94 % (3304036)Success in time 0.622 s
% 5.28/1.94 % Vampire exiting
%------------------------------------------------------------------------------