%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP560-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 2.73s 1.19s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 20 unt; 1 def)
% Number of atoms : 26 ( 16 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 : 33 ( 0 sgn 33 !; 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(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f5,definition,
( spl0_1
<=> multiply(a,b) = multiply(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( multiply(a,b) != multiply(b,a)
| 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(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(f164,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f26,f136]) ).
fof(f166,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f7,f164]) ).
fof(f167,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f166]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f167]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f173,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP560-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:07:33 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.73/1.19 % (2863167)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.73/1.19 % (2863196)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2905853045:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.73/1.19 % (2863192)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=4123516543:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.73/1.19 % (2863195)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1252747300:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.73/1.19 % (2863193)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1192220891:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.73/1.19 % (2863194)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1720498925:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.73/1.19 % (2863191)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=255231744:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.73/1.19 % (2863197)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1929349079:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.73/1.19 % (2863196)First to succeed.
% 2.73/1.19 % (2863196)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2863167"
% 2.73/1.19 % (2863197)Also succeeded, but the first one will report.
% 2.73/1.19 % (2863195)Also succeeded, but the first one will report.
% 2.73/1.19 % (2863194)Instruction limit reached!
% 2.73/1.19 % (2863194)------------------------------
% 2.73/1.19 % (2863194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.19 % (2863194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.19 % (2863194)CaDiCaL version: 2.1.3
% 2.73/1.19 % (2863194)Termination reason: Instruction limit
% 2.73/1.19 % (2863194)Termination phase: Saturation
% 2.73/1.19 % (2863194)Time elapsed: 0.095 s
% 2.73/1.19 % (2863194)Peak memory usage: 89 MB
% 2.73/1.19 % (2863194)Instructions burned: 137 (million)
% 2.73/1.19 % (2863196)Refutation found. Thanks to Tanya!
% 2.73/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.73/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.19 % (2863196)------------------------------
% 2.73/1.19 % (2863196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.19 % (2863196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.19 % (2863196)CaDiCaL version: 2.1.3
% 2.73/1.19 % (2863196)Termination reason: Refutation
% 2.73/1.19 % (2863196)Time elapsed: 0.006 s
% 2.73/1.19 % (2863196)Peak memory usage: 89 MB
% 2.73/1.19 % (2863196)Instructions burned: 13 (million)
% 2.73/1.19 % (2863196)------------------------------
% 2.73/1.19 % (2863196)------------------------------
% 2.73/1.19 % (2863167)Success in time 0.329 s
% 2.73/1.19 % Vampire exiting
%------------------------------------------------------------------------------