%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP557-1 : 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 : n002.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 10:14:51 AM UTC 2026
% Result : Unsatisfiable 2.47s 1.24s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 25 unt; 1 def)
% Number of atoms : 31 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,inverse(divide(divide(X1,X2),divide(X0,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f5,definition,
( spl0_1
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f8,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f5]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(X0,divide(divide(X1,X2),divide(X0,X2))) = X1,
inference(backward_demodulation,[],[f1,f2]) ).
fof(f11,plain,
! [X2,X0,X1] : multiply(X0,divide(divide(X2,inverse(X1)),multiply(X0,X1))) = X2,
inference(superposition,[],[f9,f2]) ).
fof(f12,plain,
! [X2,X0,X1] : multiply(X0,divide(multiply(X2,X1),multiply(X0,X1))) = X2,
inference(forward_demodulation,[],[f11,f2]) ).
fof(f14,plain,
! [X2,X3,X0,X1] : multiply(X1,divide(X0,multiply(X1,divide(divide(X0,X3),divide(X2,X3))))) = X2,
inference(superposition,[],[f12,f9]) ).
fof(f20,plain,
! [X0,X1] : multiply(X1,divide(X0,X0)) = X1,
inference(superposition,[],[f14,f9]) ).
fof(f25,plain,
! [X0,X1] : multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[],[f20,f2]) ).
fof(f26,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(superposition,[],[f14,f20]) ).
fof(f47,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[],[f26,f2]) ).
fof(f68,plain,
! [X0,X1] : multiply(inverse(divide(X1,X1)),X0) = X0,
inference(superposition,[],[f47,f20]) ).
fof(f123,plain,
! [X2,X0,X1] : divide(multiply(X0,X1),multiply(inverse(divide(X2,X2)),X1)) = X0,
inference(superposition,[],[f12,f68]) ).
fof(f136,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f123,f68]) ).
fof(f161,plain,
! [X2,X3,X0,X1] : multiply(X0,X3) = multiply(X1,divide(X2,multiply(X1,divide(divide(X2,X3),X0)))),
inference(superposition,[],[f14,f136]) ).
fof(f166,plain,
! [X2,X3] : multiply(divide(X2,X3),X3) = X2,
inference(backward_demodulation,[],[f14,f161]) ).
fof(f175,plain,
! [X0,X1] : divide(X0,X1) = multiply(inverse(X1),X0),
inference(superposition,[],[f47,f166]) ).
fof(f240,plain,
! [X2,X3] : multiply(multiply(inverse(X3),X2),X3) = X2,
inference(backward_demodulation,[],[f166,f175]) ).
fof(f447,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f240,f25]) ).
fof(f456,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f7,f447]) ).
fof(f457,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f456]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f457]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f458,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP557-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n002.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 10:10:22 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 2.47/1.24 % (3314925)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.47/1.24 % (3315007)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=675456096:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.47/1.24 % (3315007)First to succeed.
% 2.47/1.24 % (3315007)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3314925"
% 2.47/1.24 % (3315004)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=190584217:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.47/1.24 % (3315008)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1962696643:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.47/1.24 % (3315005)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4018456344:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.47/1.24 % (3315002)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=2070544058:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.47/1.24 % (3315003)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=534724203:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.47/1.24 % (3315006)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3835845993:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.47/1.24 % (3315006)Also succeeded, but the first one will report.
% 2.47/1.24 % (3315008)Also succeeded, but the first one will report.
% 2.47/1.24 % (3315005)Also succeeded, but the first one will report.
% 2.47/1.24 % (3315007)Refutation found. Thanks to Tanya!
% 2.47/1.24 % SZS status Unsatisfiable for theBenchmark
% 2.47/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/1.24 % (3315007)------------------------------
% 2.47/1.24 % (3315007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.24 % (3315007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.24 % (3315007)CaDiCaL version: 2.1.3
% 2.47/1.24 % (3315007)Termination reason: Refutation
% 2.47/1.24 % (3315007)Time elapsed: 0.011 s
% 2.47/1.24 % (3315007)Peak memory usage: 89 MB
% 2.47/1.24 % (3315007)Instructions burned: 28 (million)
% 2.47/1.24 % (3315007)------------------------------
% 2.47/1.24 % (3315007)------------------------------
% 2.47/1.24 % (3314925)Success in time 0.278 s
% 2.47/1.24 % Vampire exiting
%------------------------------------------------------------------------------