%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP458-1 : 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 : n020.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 10:14:03 AM UTC 2026
% Result : Unsatisfiable 2.67s 1.35s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 30 unt; 1 def)
% Number of atoms : 36 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(divide(X0,X0),divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
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(f5,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f6,plain,
! [X0] : divide(X0,X0) = identity,
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f8,plain,
a2 != multiply(identity,a2),
inference(reorient_equations,[],[f7]) ).
fof(f10,definition,
( spl0_1
<=> a2 = multiply(identity,a2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f12,plain,
( a2 != multiply(identity,a2)
| spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f13,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f8,f10]) ).
fof(f14,plain,
! [X2,X0,X1] : divide(divide(identity,divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(forward_demodulation,[],[f1,f6]) ).
fof(f15,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(superposition,[],[f2,f6]) ).
fof(f41,plain,
! [X0,X1] : divide(divide(identity,divide(X0,divide(X1,identity))),divide(identity,X0)) = X1,
inference(superposition,[],[f14,f6]) ).
fof(f47,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(divide(identity,identity),X1))),X1) = X0,
inference(superposition,[],[f14,f2]) ).
fof(f56,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[],[f47,f6]) ).
fof(f60,plain,
! [X0,X1] : multiply(divide(identity,divide(X0,divide(X1,identity))),X0) = X1,
inference(forward_demodulation,[],[f41,f2]) ).
fof(f63,plain,
! [X0,X1] : divide(multiply(identity,multiply(X0,X1)),X1) = X0,
inference(forward_demodulation,[],[f56,f2]) ).
fof(f64,plain,
! [X0,X1] : multiply(divide(identity,divide(X0,multiply(X1,identity))),X0) = X1,
inference(forward_demodulation,[],[f60,f15]) ).
fof(f77,plain,
! [X0] : multiply(multiply(identity,multiply(X0,identity)),identity) = X0,
inference(superposition,[],[f15,f63]) ).
fof(f124,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = multiply(multiply(identity,X0),identity),
inference(superposition,[],[f77,f77]) ).
fof(f147,plain,
! [X0,X1] : divide(identity,divide(identity,multiply(X0,identity))) = multiply(divide(identity,divide(X1,X0)),X1),
inference(superposition,[],[f64,f64]) ).
fof(f150,plain,
! [X0] : multiply(divide(identity,identity),multiply(X0,identity)) = X0,
inference(superposition,[],[f64,f6]) ).
fof(f155,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = X0,
inference(forward_demodulation,[],[f150,f6]) ).
fof(f158,plain,
! [X0,X1] : multiply(identity,multiply(X0,identity)) = multiply(divide(identity,divide(X1,X0)),X1),
inference(forward_demodulation,[],[f147,f2]) ).
fof(f161,plain,
! [X0] : multiply(multiply(identity,X0),identity) = X0,
inference(backward_demodulation,[],[f124,f155]) ).
fof(f162,plain,
! [X0,X1] : multiply(divide(identity,divide(X1,X0)),X1) = X0,
inference(forward_demodulation,[],[f158,f155]) ).
fof(f163,plain,
! [X1] : multiply(X1,identity) = X1,
inference(backward_demodulation,[],[f64,f162]) ).
fof(f172,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[],[f161,f163]) ).
fof(f173,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f12,f172]) ).
fof(f193,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f173]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f13]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f193]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f203,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP458-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:06:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 2.67/1.35 % (3150075)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.67/1.35 % (3150125)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1701001972:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.67/1.35 % (3150125)First to succeed.
% 2.67/1.35 % (3150125)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3150075"
% 2.67/1.35 % (3150118)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=2440771537:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.67/1.35 % (3150121)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1659597738:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.67/1.35 % (3150123)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=868518846:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.67/1.35 % (3150126)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2732488416:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.67/1.35 % (3150115)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=3879224442:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.67/1.35 % (3150120)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2464412667:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.67/1.35 % (3150126)Also succeeded, but the first one will report.
% 2.67/1.35 % (3150123)Also succeeded, but the first one will report.
% 2.67/1.35 % (3150121)Also succeeded, but the first one will report.
% 2.67/1.35 % (3150125)Refutation found. Thanks to Tanya!
% 2.67/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.35 % (3150125)------------------------------
% 2.67/1.35 % (3150125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.35 % (3150125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.35 % (3150125)CaDiCaL version: 2.1.3
% 2.67/1.35 % (3150125)Termination reason: Refutation
% 2.67/1.35 % (3150125)Time elapsed: 0.005 s
% 2.67/1.35 % (3150125)Peak memory usage: 89 MB
% 2.67/1.35 % (3150125)Instructions burned: 12 (million)
% 2.67/1.35 % (3150125)------------------------------
% 2.67/1.35 % (3150125)------------------------------
% 2.67/1.35 % (3150075)Success in time 0.296 s
% 2.67/1.35 % Vampire exiting
%------------------------------------------------------------------------------