%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.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 10:17:09 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 107 ( 29 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 106 ( 42 ~; 40 |; 18 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 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 : 50 ( 45 !; 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(f15,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f3]) ).
fof(f16,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(f17,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X0,f)
| ~ group_member(X1,f) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ? [X1] :
( group_member(X1,f)
& phi(X1) = X0 )
| ~ group_member(X0,h) ),
inference(ennf_transformation,[],[f5]) ).
fof(f19,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))],[f18]) ).
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,[],[f19]) ).
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(f27,plain,
! [X0] :
( ~ group_member(X0,f)
| group_member(phi(X0),h) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ~ group_member(X0,f)
| multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0] :
( ~ group_member(X0,h)
| phi(sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0] :
( ~ group_member(X0,h)
| group_member(sK0(X0),f) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ left_zero(X0,X1)
| ~ group_member(X3,X0)
| multiply(X0,X1,X3) = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X0,X1] :
( ~ left_zero(X0,X1)
| group_member(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X0,X1] :
( ~ group_member(X1,X0)
| left_zero(X0,X1)
| group_member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X0,X1] :
( ~ group_member(X1,X0)
| left_zero(X0,X1)
| multiply(X0,X1,sK1(X0,X1)) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[],[f7]) ).
fof(f36,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[],[f10]) ).
fof(f37,plain,
group_member(f_left_zero,f),
inference(resolution,[],[f32,f35]) ).
fof(f38,plain,
group_member(phi(f_left_zero),h),
inference(resolution,[],[f37,f27]) ).
fof(f44,plain,
( left_zero(h,phi(f_left_zero))
| group_member(sK1(h,phi(f_left_zero)),h) ),
inference(resolution,[],[f33,f38]) ).
fof(f55,plain,
group_member(sK1(h,phi(f_left_zero)),h),
inference(forward_subsumption_resolution,[],[f44,f36]) ).
fof(f56,plain,
sK1(h,phi(f_left_zero)) = phi(sK0(sK1(h,phi(f_left_zero)))),
inference(resolution,[],[f55,f29]) ).
fof(f57,plain,
group_member(sK0(sK1(h,phi(f_left_zero))),f),
inference(resolution,[],[f55,f30]) ).
fof(f85,plain,
! [X0] :
( ~ group_member(X0,f)
| f_left_zero = multiply(f,f_left_zero,X0) ),
inference(resolution,[],[f31,f35]) ).
fof(f99,plain,
( left_zero(h,phi(f_left_zero))
| phi(f_left_zero) != multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))) ),
inference(resolution,[],[f34,f38]) ).
fof(f120,plain,
phi(f_left_zero) != multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))),
inference(forward_subsumption_resolution,[],[f99,f36]) ).
fof(f139,plain,
! [X0] :
( ~ group_member(X0,f)
| multiply(h,phi(f_left_zero),phi(X0)) = phi(multiply(f,f_left_zero,X0)) ),
inference(resolution,[],[f28,f37]) ).
fof(f176,plain,
f_left_zero = multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero)))),
inference(resolution,[],[f85,f57]) ).
fof(f208,plain,
multiply(h,phi(f_left_zero),phi(sK0(sK1(h,phi(f_left_zero))))) = phi(multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero))))),
inference(resolution,[],[f139,f57]) ).
fof(f211,plain,
phi(f_left_zero) = multiply(h,phi(f_left_zero),phi(sK0(sK1(h,phi(f_left_zero))))),
inference(forward_demodulation,[],[f208,f176]) ).
fof(f214,plain,
phi(f_left_zero) = multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))),
inference(forward_demodulation,[],[f211,f56]) ).
fof(f216,plain,
$false,
inference(forward_subsumption_resolution,[],[f214,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.38 % Computer : n020.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 09:38:05 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 Running first-order model finding
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (3141417)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3141436)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1480847512:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (3141431)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3141431)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3366108859:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3141433)dis+10_1_sil=32000:sp=arity:random_seed=3316852786:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3141434)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2967506974:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3141430)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=537179976_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3141432)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=18435113:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3141435)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2868064914:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % (3141435) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3141417-3141435"...
% 0.17/0.48 % (3141435)...printing done.
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (3141435)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3141435)------------------------------
% 0.17/0.48 % (3141435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3141435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3141435)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3141435)Termination reason: Refutation
% 0.17/0.48 % (3141435)Time elapsed: 0.005 s
% 0.17/0.48 % (3141435)Peak memory usage: 11 MB
% 0.17/0.48 % (3141435)Instructions burned: 6 (million)
% 0.17/0.48 % (3141417)Success in time 0.049 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------