%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP550-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 10:14:50 AM UTC 2026
% Result : Unsatisfiable 2.71s 1.39s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 36 unt; 3 def)
% Number of atoms : 75 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 17 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(identity,X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = divide(identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,plain,
! [X0] : divide(identity,X0) = inverse(X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f6,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f7,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f6]) ).
fof(f9,definition,
( spl0_1
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f11,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f7,f9]) ).
fof(f13,plain,
! [X2,X0,X1] : divide(inverse(X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(backward_demodulation,[],[f1,f4]) ).
fof(f14,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f4]) ).
fof(f16,plain,
identity = inverse(identity),
inference(superposition,[],[f5,f4]) ).
fof(f18,definition,
( spl0_2
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f20,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f21,plain,
spl0_2,
inference(avatar_split_clause,[],[f16,f18]) ).
fof(f24,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(superposition,[],[f5,f14]) ).
fof(f25,plain,
! [X0] : inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[],[f4,f14]) ).
fof(f28,plain,
! [X0,X1] : inverse(inverse(X1)) = multiply(multiply(inverse(X0),X0),X1),
inference(superposition,[],[f25,f24]) ).
fof(f29,plain,
( a2 != inverse(inverse(a2))
| spl0_1 ),
inference(backward_demodulation,[],[f11,f28]) ).
fof(f31,definition,
( spl0_3
<=> a2 = inverse(inverse(a2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f33,plain,
( a2 != inverse(inverse(a2))
| spl0_3 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
( ~ spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f29,f9,f31]) ).
fof(f35,plain,
! [X0,X1] : divide(inverse(X0),divide(divide(identity,X1),X0)) = X1,
inference(superposition,[],[f13,f5]) ).
fof(f36,plain,
! [X0,X1] : divide(inverse(X0),divide(divide(inverse(X0),X1),identity)) = X1,
inference(superposition,[],[f13,f4]) ).
fof(f39,plain,
! [X0,X1] : divide(X1,X0) = divide(inverse(X0),divide(identity,X1)),
inference(superposition,[],[f13,f5]) ).
fof(f42,plain,
! [X0,X1] : divide(X1,X0) = divide(inverse(X0),inverse(X1)),
inference(forward_demodulation,[],[f39,f4]) ).
fof(f44,plain,
! [X0,X1] : divide(inverse(X0),divide(inverse(X1),X0)) = X1,
inference(forward_demodulation,[],[f35,f4]) ).
fof(f45,plain,
! [X0,X1] : divide(X1,X0) = multiply(inverse(X0),X1),
inference(forward_demodulation,[],[f42,f14]) ).
fof(f47,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),identity),
inference(backward_demodulation,[],[f4,f45]) ).
fof(f53,plain,
! [X0,X1] : divide(inverse(X0),multiply(inverse(X0),inverse(X1))) = X1,
inference(backward_demodulation,[],[f44,f45]) ).
fof(f54,plain,
! [X0,X1] : divide(inverse(X0),divide(multiply(inverse(X1),inverse(X0)),identity)) = X1,
inference(backward_demodulation,[],[f36,f45]) ).
fof(f56,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X1)),X0),
inference(backward_demodulation,[],[f14,f45]) ).
fof(f58,plain,
! [X0,X1] : multiply(inverse(divide(multiply(inverse(X1),inverse(X0)),identity)),inverse(X0)) = X1,
inference(forward_demodulation,[],[f54,f45]) ).
fof(f59,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),inverse(X1))),inverse(X0)) = X1,
inference(forward_demodulation,[],[f53,f45]) ).
fof(f65,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(identity),multiply(inverse(X1),inverse(X0)))),inverse(X0)) = X1,
inference(forward_demodulation,[],[f58,f45]) ).
fof(f70,plain,
( ! [X0,X1] : multiply(inverse(multiply(identity,multiply(inverse(X1),inverse(X0)))),inverse(X0)) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f65,f20]) ).
fof(f73,plain,
( ! [X0,X1] : multiply(inverse(inverse(inverse(multiply(inverse(X1),inverse(X0))))),inverse(X0)) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f70,f25]) ).
fof(f84,plain,
! [X0] : inverse(X0) = multiply(inverse(inverse(identity)),inverse(X0)),
inference(superposition,[],[f47,f56]) ).
fof(f88,plain,
( ! [X0] : inverse(X0) = multiply(inverse(identity),inverse(X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f84,f20]) ).
fof(f90,plain,
( ! [X0] : inverse(X0) = multiply(identity,inverse(X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f88,f20]) ).
fof(f92,plain,
( ! [X0] : inverse(X0) = inverse(inverse(inverse(X0)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f90,f25]) ).
fof(f94,plain,
( ! [X0,X1] : multiply(inverse(multiply(inverse(X1),inverse(X0))),inverse(X0)) = X1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f73,f92]) ).
fof(f231,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(inverse(inverse(X0))),inverse(X1))),inverse(X1)) = X0,
inference(superposition,[],[f59,f56]) ).
fof(f239,plain,
( ! [X0] : inverse(inverse(X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f231,f94]) ).
fof(f245,plain,
( $false
| ~ spl0_2
| spl0_3 ),
inference(backward_subsumption_resolution,[],[f33,f239]) ).
fof(f259,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f245]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f12]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f21]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f34]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f259]) ).
cnf(s6,plain,
spl0_3,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f267,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP550-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.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 10:12:45 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.71/1.39 % (3330701)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.71/1.39 % (3330812)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1024449085:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.71/1.39 % (3330812)First to succeed.
% 2.71/1.39 % (3330812)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3330701"
% 2.71/1.39 % (3330809)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=993369232:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.71/1.39 % (3330811)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4039889691:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.71/1.39 % (3330807)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=208359679:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.71/1.39 % (3330808)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=222518417:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.71/1.39 % (3330810)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2544857679:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.71/1.39 % (3330811)Also succeeded, but the first one will report.
% 2.71/1.39 % (3330810)Also succeeded, but the first one will report.
% 2.71/1.39 % (3330813)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3585798454:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.71/1.39 % (3330813)Also succeeded, but the first one will report.
% 2.71/1.39 % (3330812)Refutation found. Thanks to Tanya!
% 2.71/1.39 % SZS status Unsatisfiable for theBenchmark
% 2.71/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.39 % (3330812)------------------------------
% 2.71/1.39 % (3330812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.39 % (3330812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.39 % (3330812)CaDiCaL version: 2.1.3
% 2.71/1.39 % (3330812)Termination reason: Refutation
% 2.71/1.39 % (3330812)Time elapsed: 0.006 s
% 2.71/1.39 % (3330812)Peak memory usage: 89 MB
% 2.71/1.39 % (3330812)Instructions burned: 13 (million)
% 2.71/1.39 % (3330812)------------------------------
% 2.71/1.39 % (3330812)------------------------------
% 2.71/1.39 % (3330701)Success in time 0.3 s
% 2.71/1.39 % Vampire exiting
%------------------------------------------------------------------------------