%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP459-1 : 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 : n012.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 2.33s 0.95s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 51 unt; 1 def)
% Number of atoms : 57 ( 47 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 : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 93 !; 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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f5,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f6,plain,
! [X0] : divide(X0,X0) = identity,
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f9,definition,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f11,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| 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(divide(identity,divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(forward_demodulation,[],[f1,f6]) ).
fof(f14,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(superposition,[],[f2,f6]) ).
fof(f15,plain,
! [X0,X1] : multiply(X1,divide(identity,X0)) = divide(X1,multiply(identity,X0)),
inference(superposition,[],[f2,f2]) ).
fof(f39,plain,
! [X2,X3,X0,X1] : divide(divide(identity,divide(divide(X1,divide(X0,divide(divide(identity,X1),X2))),divide(X3,X0))),X2) = X3,
inference(superposition,[],[f13,f13]) ).
fof(f40,plain,
! [X0,X1] : divide(divide(identity,divide(X0,divide(X1,identity))),divide(identity,X0)) = X1,
inference(superposition,[],[f13,f6]) ).
fof(f46,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(divide(identity,identity),X1))),X1) = X0,
inference(superposition,[],[f13,f2]) ).
fof(f49,plain,
! [X2,X0,X1] : multiply(divide(identity,divide(X1,divide(X0,divide(divide(identity,X1),divide(identity,X2))))),X2) = X0,
inference(superposition,[],[f2,f13]) ).
fof(f52,plain,
! [X2,X0,X1] : multiply(divide(identity,divide(X1,divide(X0,multiply(divide(identity,X1),X2)))),X2) = X0,
inference(forward_demodulation,[],[f49,f2]) ).
fof(f55,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[],[f46,f6]) ).
fof(f59,plain,
! [X0,X1] : multiply(divide(identity,divide(X0,divide(X1,identity))),X0) = X1,
inference(forward_demodulation,[],[f40,f2]) ).
fof(f62,plain,
! [X0,X1] : divide(multiply(identity,multiply(X0,X1)),X1) = X0,
inference(forward_demodulation,[],[f55,f2]) ).
fof(f63,plain,
! [X0,X1] : multiply(divide(identity,divide(X0,multiply(X1,identity))),X0) = X1,
inference(forward_demodulation,[],[f59,f14]) ).
fof(f75,plain,
! [X2,X0,X1] : multiply(identity,multiply(X0,divide(divide(identity,X1),X2))) = divide(divide(identity,divide(X1,X0)),X2),
inference(superposition,[],[f13,f62]) ).
fof(f76,plain,
! [X0] : multiply(multiply(identity,multiply(X0,identity)),identity) = X0,
inference(superposition,[],[f14,f62]) ).
fof(f77,plain,
! [X2,X0,X1] : multiply(identity,multiply(divide(X1,divide(divide(identity,X0),X2)),divide(divide(identity,X0),X2))) = X1,
inference(backward_demodulation,[],[f13,f75]) ).
fof(f79,plain,
! [X2,X3,X0,X1] : multiply(identity,multiply(divide(X3,X0),divide(divide(identity,divide(X1,divide(X0,divide(divide(identity,X1),X2)))),X2))) = X3,
inference(backward_demodulation,[],[f39,f75]) ).
fof(f84,plain,
! [X2,X3,X0,X1] : multiply(identity,multiply(divide(X3,X0),multiply(identity,multiply(divide(X0,divide(divide(identity,X1),X2)),divide(divide(identity,X1),X2))))) = X3,
inference(forward_demodulation,[],[f79,f75]) ).
fof(f87,plain,
! [X3,X0] : multiply(identity,multiply(divide(X3,X0),X0)) = X3,
inference(forward_demodulation,[],[f84,f77]) ).
fof(f88,plain,
! [X0] : multiply(identity,multiply(identity,X0)) = X0,
inference(superposition,[],[f87,f6]) ).
fof(f106,plain,
! [X0,X1] : divide(X1,multiply(identity,multiply(identity,X0))) = multiply(X1,multiply(identity,divide(identity,X0))),
inference(superposition,[],[f15,f15]) ).
fof(f119,plain,
! [X0,X1] : divide(X1,X0) = multiply(X1,multiply(identity,divide(identity,X0))),
inference(forward_demodulation,[],[f106,f88]) ).
fof(f123,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = multiply(multiply(identity,X0),identity),
inference(superposition,[],[f76,f76]) ).
fof(f148,plain,
! [X0,X1] : divide(identity,divide(identity,multiply(X0,identity))) = multiply(divide(identity,divide(X1,X0)),X1),
inference(superposition,[],[f63,f63]) ).
fof(f151,plain,
! [X0] : multiply(divide(identity,identity),multiply(X0,identity)) = X0,
inference(superposition,[],[f63,f6]) ).
fof(f154,plain,
! [X0,X1] : divide(multiply(identity,X0),X1) = divide(identity,divide(X1,multiply(X0,identity))),
inference(superposition,[],[f62,f63]) ).
fof(f156,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = X0,
inference(forward_demodulation,[],[f151,f6]) ).
fof(f159,plain,
! [X0,X1] : multiply(identity,multiply(X0,identity)) = multiply(divide(identity,divide(X1,X0)),X1),
inference(forward_demodulation,[],[f148,f2]) ).
fof(f162,plain,
! [X0] : multiply(multiply(identity,X0),identity) = X0,
inference(backward_demodulation,[],[f123,f156]) ).
fof(f163,plain,
! [X0,X1] : multiply(divide(identity,divide(X1,X0)),X1) = X0,
inference(forward_demodulation,[],[f159,f156]) ).
fof(f164,plain,
! [X1] : multiply(X1,identity) = X1,
inference(backward_demodulation,[],[f63,f163]) ).
fof(f169,plain,
! [X0,X1] : divide(identity,divide(X1,X0)) = divide(multiply(identity,X0),X1),
inference(backward_demodulation,[],[f154,f164]) ).
fof(f173,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[],[f162,f164]) ).
fof(f185,plain,
! [X0,X1] : multiply(X1,divide(identity,X0)) = divide(X1,X0),
inference(backward_demodulation,[],[f119,f173]) ).
fof(f187,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(backward_demodulation,[],[f62,f173]) ).
fof(f191,plain,
! [X0,X1] : divide(identity,divide(X1,X0)) = divide(X0,X1),
inference(forward_demodulation,[],[f169,f173]) ).
fof(f340,plain,
! [X0,X1] : multiply(X1,divide(identity,X0)) = divide(identity,divide(X0,X1)),
inference(superposition,[],[f185,f191]) ).
fof(f347,plain,
! [X2,X0,X1] : multiply(multiply(divide(X0,multiply(divide(identity,X1),X2)),divide(identity,X1)),X2) = X0,
inference(backward_demodulation,[],[f52,f340]) ).
fof(f533,plain,
! [X2,X0,X1] : multiply(multiply(divide(X1,multiply(multiply(identity,X0),X2)),multiply(identity,X0)),X2) = X1,
inference(superposition,[],[f347,f2]) ).
fof(f556,plain,
! [X2,X0,X1] : multiply(multiply(divide(X1,multiply(X0,X2)),X0),X2) = X1,
inference(forward_demodulation,[],[f533,f173]) ).
fof(f908,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[],[f556,f187]) ).
fof(f936,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f11,f908]) ).
fof(f949,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f936]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f12]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f949]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f1011,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP459-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 10:04:50 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.33 Running first-order theorem proving
% 0.09/0.33 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
% 2.33/0.95 % (2139112)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.33/0.95 % (2139212)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=77511119:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.33/0.95 % (2139216)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3577085148:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.33/0.95 % (2139218)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3065360975:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.33/0.95 % (2139219)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=469437131:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.33/0.95 % (2139214)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=892616426:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.33/0.95 % (2139213)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=3279132515:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.33/0.95 % (2139215)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1091037405:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.33/0.95 % (2139218)First to succeed.
% 2.33/0.95 % (2139218)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2139112"
% 2.33/0.95 % (2139219)Also succeeded, but the first one will report.
% 2.33/0.95 % (2139215)Also succeeded, but the first one will report.
% 2.33/0.95 % (2139216)Instruction limit reached!
% 2.33/0.95 % (2139216)------------------------------
% 2.33/0.95 % (2139216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.95 % (2139216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.95 % (2139216)CaDiCaL version: 2.1.3
% 2.33/0.95 % (2139216)Termination reason: Instruction limit
% 2.33/0.95 % (2139216)Termination phase: Saturation
% 2.33/0.95 % (2139216)Time elapsed: 0.054 s
% 2.33/0.95 % (2139216)Peak memory usage: 89 MB
% 2.33/0.95 % (2139216)Instructions burned: 182 (million)
% 2.33/0.95 % (2139218)Refutation found. Thanks to Tanya!
% 2.33/0.95 % SZS status Unsatisfiable for theBenchmark
% 2.33/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.95 % (2139218)------------------------------
% 2.33/0.95 % (2139218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.95 % (2139218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.95 % (2139218)CaDiCaL version: 2.1.3
% 2.33/0.95 % (2139218)Termination reason: Refutation
% 2.33/0.95 % (2139218)Time elapsed: 0.014 s
% 2.33/0.95 % (2139218)Peak memory usage: 89 MB
% 2.33/0.95 % (2139218)Instructions burned: 38 (million)
% 2.33/0.95 % (2139218)------------------------------
% 2.33/0.95 % (2139218)------------------------------
% 2.33/0.95 % (2139112)Success in time 0.309 s
% 2.33/0.95 % Vampire exiting
%------------------------------------------------------------------------------