%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP494-1 : 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 : n005.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 10:14:08 AM UTC 2026
% Result : Unsatisfiable 2.50s 1.38s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 35 unt; 2 def)
% Number of atoms : 72 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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 : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f6,plain,
a2 != multiply(identity,a2),
inference(reorient_equations,[],[f5]) ).
fof(f8,definition,
( spl0_1
<=> a2 = multiply(identity,a2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f10,plain,
( a2 != multiply(identity,a2)
| spl0_1 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f11,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f6,f8]) ).
fof(f12,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),inverse(identity)),double_divide(X0,X2))) = X1,
inference(backward_demodulation,[],[f1,f3]) ).
fof(f13,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f13,f3]) ).
fof(f15,plain,
! [X0] : inverse(identity) = multiply(inverse(X0),X0),
inference(superposition,[],[f13,f4]) ).
fof(f17,plain,
! [X0,X1] : multiply(identity,double_divide(X1,X0)) = inverse(multiply(X0,X1)),
inference(superposition,[],[f14,f13]) ).
fof(f31,plain,
! [X0] : identity = double_divide(identity,multiply(inverse(X0),X0)),
inference(superposition,[],[f4,f15]) ).
fof(f35,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,inverse(identity)),double_divide(X0,inverse(X1)))) = X1,
inference(superposition,[],[f12,f4]) ).
fof(f38,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,identity),inverse(identity)),inverse(X0))) = X1,
inference(superposition,[],[f12,f3]) ).
fof(f43,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),inverse(identity)),inverse(X0))) = X1,
inference(forward_demodulation,[],[f38,f3]) ).
fof(f44,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[],[f35,f4]) ).
fof(f63,plain,
! [X0,X1] : double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X0,multiply(inverse(X1),X1)),inverse(identity)),identity)) = X0,
inference(superposition,[],[f12,f31]) ).
fof(f68,plain,
! [X0,X1] : double_divide(double_divide(identity,identity),inverse(double_divide(double_divide(X0,multiply(inverse(X1),X1)),inverse(identity)))) = X0,
inference(forward_demodulation,[],[f63,f3]) ).
fof(f71,plain,
! [X0,X1] : double_divide(double_divide(identity,identity),multiply(inverse(identity),double_divide(X0,multiply(inverse(X1),X1)))) = X0,
inference(forward_demodulation,[],[f68,f13]) ).
fof(f72,plain,
! [X0,X1] : double_divide(inverse(identity),multiply(inverse(identity),double_divide(X0,multiply(inverse(X1),X1)))) = X0,
inference(forward_demodulation,[],[f71,f3]) ).
fof(f98,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = X0,
inference(superposition,[],[f44,f4]) ).
fof(f104,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = X0,
inference(forward_demodulation,[],[f98,f3]) ).
fof(f105,plain,
! [X0] : multiply(inverse(X0),X0) = double_divide(identity,inverse(identity)),
inference(superposition,[],[f104,f31]) ).
fof(f107,plain,
inverse(identity) = double_divide(identity,inverse(identity)),
inference(superposition,[],[f104,f4]) ).
fof(f113,plain,
! [X0,X1] : double_divide(identity,X0) = double_divide(double_divide(identity,X1),double_divide(double_divide(X0,inverse(identity)),double_divide(X1,inverse(identity)))),
inference(superposition,[],[f12,f104]) ).
fof(f116,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f107,f4]) ).
fof(f122,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f105,f4]) ).
fof(f124,definition,
( spl0_4
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f126,plain,
( identity = inverse(identity)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
spl0_4,
inference(avatar_split_clause,[],[f116,f124]) ).
fof(f137,plain,
( ! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),identity),inverse(X0))) = X1
| ~ spl0_4 ),
inference(backward_demodulation,[],[f43,f126]) ).
fof(f141,plain,
( ! [X0,X1] : double_divide(identity,multiply(identity,double_divide(X0,multiply(inverse(X1),X1)))) = X0
| ~ spl0_4 ),
inference(backward_demodulation,[],[f72,f126]) ).
fof(f149,plain,
( ! [X0,X1] : double_divide(identity,X0) = double_divide(double_divide(identity,X1),double_divide(double_divide(X0,identity),double_divide(X1,identity)))
| ~ spl0_4 ),
inference(backward_demodulation,[],[f113,f126]) ).
fof(f154,plain,
( ! [X0,X1] : double_divide(identity,X0) = double_divide(double_divide(identity,X1),double_divide(double_divide(X0,identity),inverse(X1)))
| ~ spl0_4 ),
inference(forward_demodulation,[],[f149,f3]) ).
fof(f160,plain,
( ! [X0,X1] : double_divide(identity,inverse(multiply(multiply(inverse(X1),X1),X0))) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f141,f17]) ).
fof(f164,plain,
( ! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(inverse(X1)),inverse(X0))) = X1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f137,f3]) ).
fof(f172,plain,
( ! [X0,X1] : double_divide(identity,X0) = double_divide(double_divide(identity,X1),double_divide(inverse(X0),inverse(X1)))
| ~ spl0_4 ),
inference(forward_demodulation,[],[f154,f3]) ).
fof(f184,plain,
( ! [X1] : double_divide(identity,inverse(X1)) = X1
| ~ spl0_4 ),
inference(backward_demodulation,[],[f164,f172]) ).
fof(f191,plain,
( ! [X0,X1] : multiply(multiply(inverse(X1),X1),X0) = X0
| ~ spl0_4 ),
inference(backward_demodulation,[],[f160,f184]) ).
fof(f216,plain,
! [X0,X1] : inverse(inverse(X1)) = multiply(multiply(inverse(X0),X0),X1),
inference(superposition,[],[f14,f122]) ).
fof(f227,plain,
( ! [X1] : inverse(inverse(X1)) = X1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f216,f191]) ).
fof(f238,plain,
( ! [X0] : multiply(identity,X0) = X0
| ~ spl0_4 ),
inference(backward_demodulation,[],[f14,f227]) ).
fof(f243,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(backward_subsumption_resolution,[],[f10,f238]) ).
fof(f252,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f243]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f11]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f127]) ).
cnf(s7,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f252]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s7,s4]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8]) ).
fof(f386,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP494-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:05:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.50/1.38 % (3764183)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.50/1.38 % (3764208)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1489636805:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.50/1.38 % (3764208)First to succeed.
% 2.50/1.38 % (3764208)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3764183"
% 2.50/1.38 % (3764204)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=2777690005:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.50/1.38 % (3764203)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=1670027192:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.50/1.38 % (3764205)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2833501523:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.50/1.38 % (3764206)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=845157494:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.50/1.38 % (3764206)Also succeeded, but the first one will report.
% 2.50/1.38 % (3764209)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1410357940:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.50/1.38 % (3764207)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1762723857:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.50/1.38 % (3764209)Also succeeded, but the first one will report.
% 2.50/1.38 % (3764207)Also succeeded, but the first one will report.
% 2.50/1.38 % (3764208)Refutation found. Thanks to Tanya!
% 2.50/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.50/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.39 % (3764208)------------------------------
% 2.50/1.39 % (3764208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.39 % (3764208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.39 % (3764208)CaDiCaL version: 2.1.3
% 2.50/1.39 % (3764208)Termination reason: Refutation
% 2.50/1.39 % (3764208)Time elapsed: 0.008 s
% 2.50/1.39 % (3764208)Peak memory usage: 89 MB
% 2.50/1.39 % (3764208)Instructions burned: 19 (million)
% 2.50/1.39 % (3764208)------------------------------
% 2.50/1.39 % (3764208)------------------------------
% 2.50/1.39 % (3764183)Success in time 0.262 s
% 2.50/1.39 % Vampire exiting
%------------------------------------------------------------------------------