%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP446-1 : TPTP v9.3.1. Released v2.6.0.
% 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 10:14:01 AM UTC 2026
% Result : Unsatisfiable 3.86s 1.65s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 33 unt; 2 def)
% Number of atoms : 49 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 6 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f5,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f4]) ).
fof(f7,definition,
( spl0_1
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f10,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f5,f7]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f12,plain,
! [X2,X0,X1] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[],[f1,f3]) ).
fof(f13,plain,
! [X2,X0,X1] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[],[f12,f3]) ).
fof(f14,plain,
! [X0,X1] : inverse(X1) = divide(inverse(divide(X0,X0)),X1),
inference(superposition,[],[f3,f3]) ).
fof(f16,plain,
! [X0,X1] : inverse(X1) = divide(multiply(inverse(X0),X0),X1),
inference(superposition,[],[f3,f11]) ).
fof(f17,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(superposition,[],[f3,f11]) ).
fof(f23,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(divide(X1,X1)),X0),
inference(superposition,[],[f11,f14]) ).
fof(f27,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(multiply(inverse(X1),X1),X0),
inference(superposition,[],[f11,f16]) ).
fof(f28,plain,
( a2 != inverse(inverse(a2))
| spl0_1 ),
inference(backward_demodulation,[],[f9,f27]) ).
fof(f30,definition,
( spl0_2
<=> a2 = inverse(inverse(a2)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f32,plain,
( a2 != inverse(inverse(a2))
| spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f33,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f28,f7,f30]) ).
fof(f42,plain,
! [X2,X0,X1] : divide(X0,divide(divide(inverse(X2),inverse(X1)),multiply(inverse(X0),X1))) = X2,
inference(superposition,[],[f13,f11]) ).
fof(f44,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(superposition,[],[f13,f3]) ).
fof(f57,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[],[f44,f11]) ).
fof(f58,plain,
! [X2,X0,X1] : divide(X0,divide(multiply(inverse(X2),X1),multiply(inverse(X0),X1))) = X2,
inference(forward_demodulation,[],[f42,f11]) ).
fof(f67,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f57,f11]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(inverse(X1)),X0) = multiply(X1,X0),
inference(superposition,[],[f67,f67]) ).
fof(f71,plain,
! [X0,X1] : inverse(inverse(multiply(inverse(divide(X1,X1)),X0))) = X0,
inference(superposition,[],[f17,f67]) ).
fof(f72,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[],[f71,f23]) ).
fof(f79,plain,
! [X0,X1] : multiply(X1,inverse(inverse(inverse(X0)))) = divide(X1,X0),
inference(superposition,[],[f11,f72]) ).
fof(f91,plain,
! [X2,X0,X1] : multiply(X0,inverse(inverse(inverse(divide(multiply(inverse(X2),X1),multiply(inverse(X0),X1)))))) = X2,
inference(backward_demodulation,[],[f58,f79]) ).
fof(f103,plain,
! [X2,X0,X1] : multiply(X0,inverse(inverse(inverse(multiply(multiply(inverse(X2),X1),inverse(inverse(inverse(multiply(inverse(X0),X1))))))))) = X2,
inference(forward_demodulation,[],[f91,f79]) ).
fof(f183,plain,
! [X2,X0,X1] : inverse(X0) = multiply(X2,inverse(inverse(inverse(multiply(multiply(X0,X1),inverse(inverse(inverse(multiply(inverse(X2),X1))))))))),
inference(superposition,[],[f103,f69]) ).
fof(f213,plain,
! [X2] : inverse(inverse(X2)) = X2,
inference(backward_demodulation,[],[f103,f183]) ).
fof(f239,plain,
( $false
| spl0_2 ),
inference(backward_subsumption_resolution,[],[f32,f213]) ).
fof(f243,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f239]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f243]) ).
cnf(s4,plain,
spl0_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f273,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP446-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n001.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 10:10:46 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.47 Running first-order theorem proving
% 0.17/0.47 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
% 3.86/1.65 % (3324186)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.86/1.65 % (3324202)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3748316066:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.86/1.65 % (3324206)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=980278569:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.86/1.65 % (3324205)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3718855641:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.86/1.65 % (3324201)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3718381792:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.86/1.65 % (3324203)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2264130433:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.86/1.65 % (3324207)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=240277181:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.86/1.65 % (3324204)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3883995375:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.86/1.65 % (3324206)First to succeed.
% 3.86/1.65 % (3324206)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3324186"
% 3.86/1.65 % (3324207)Also succeeded, but the first one will report.
% 3.86/1.65 % (3324205)Also succeeded, but the first one will report.
% 3.86/1.65 % (3324204)Instruction limit reached!
% 3.86/1.65 % (3324204)------------------------------
% 3.86/1.65 % (3324204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.65 % (3324204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.65 % (3324204)CaDiCaL version: 2.1.3
% 3.86/1.65 % (3324204)Termination reason: Instruction limit
% 3.86/1.65 % (3324204)Termination phase: Saturation
% 3.86/1.65 % (3324204)Time elapsed: 0.079 s
% 3.86/1.65 % (3324204)Peak memory usage: 89 MB
% 3.86/1.65 % (3324204)Instructions burned: 136 (million)
% 3.86/1.65 % (3324216)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=555849113:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.86/1.65 % (3324206)Refutation found. Thanks to Tanya!
% 3.86/1.65 % SZS status Unsatisfiable for theBenchmark
% 3.86/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 3.86/1.65 % (3324206)------------------------------
% 3.86/1.65 % (3324206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.65 % (3324206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.65 % (3324206)CaDiCaL version: 2.1.3
% 3.86/1.65 % (3324206)Termination reason: Refutation
% 3.86/1.65 % (3324206)Time elapsed: 0.012 s
% 3.86/1.65 % (3324206)Peak memory usage: 89 MB
% 3.86/1.65 % (3324206)Instructions burned: 17 (million)
% 3.86/1.65 % (3324206)------------------------------
% 3.86/1.65 % (3324206)------------------------------
% 3.86/1.65 % (3324186)Success in time 0.429 s
% 3.86/1.65 % Vampire exiting
%------------------------------------------------------------------------------