%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP535-1 : 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 : n002.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 10:14:48 AM UTC 2026
% Result : Unsatisfiable 3.43s 1.38s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 35 unt; 3 def)
% Number of atoms : 74 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 19 ~; 17 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,divide(divide(X0,X1),X2)),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f7,definition,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f10,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f5,f7]) ).
fof(f11,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(forward_demodulation,[],[f3,f4]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(forward_demodulation,[],[f2,f4]) ).
fof(f13,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f12,f11]) ).
fof(f15,plain,
identity = inverse(identity),
inference(superposition,[],[f4,f11]) ).
fof(f17,definition,
( spl0_2
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f19,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f20,plain,
spl0_2,
inference(avatar_split_clause,[],[f15,f17]) ).
fof(f23,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(superposition,[],[f4,f13]) ).
fof(f24,plain,
! [X0] : inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[],[f11,f13]) ).
fof(f25,plain,
! [X0,X1] : divide(divide(X0,divide(identity,X1)),X0) = X1,
inference(superposition,[],[f1,f4]) ).
fof(f34,plain,
! [X2,X0,X1] : multiply(divide(X1,divide(divide(X1,inverse(X2)),X0)),X2) = X0,
inference(superposition,[],[f13,f1]) ).
fof(f35,plain,
! [X2,X0,X1] : multiply(divide(X1,divide(multiply(X1,X2),X0)),X2) = X0,
inference(forward_demodulation,[],[f34,f13]) ).
fof(f40,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[],[f25,f11]) ).
fof(f41,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[],[f40,f13]) ).
fof(f43,plain,
( ! [X0] : divide(X0,identity) = multiply(X0,identity)
| ~ spl0_2 ),
inference(superposition,[],[f13,f19]) ).
fof(f47,plain,
! [X0] : divide(identity,inverse(X0)) = X0,
inference(superposition,[],[f41,f23]) ).
fof(f48,plain,
! [X0] : divide(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f41,f24]) ).
fof(f52,plain,
( ! [X0] : multiply(inverse(inverse(X0)),identity) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f48,f43]) ).
fof(f53,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f47,f13]) ).
fof(f54,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f53,f24]) ).
fof(f55,plain,
( ! [X0] : multiply(X0,identity) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f52,f54]) ).
fof(f61,plain,
! [X0,X1] : divide(X1,X0) = multiply(X1,inverse(X0)),
inference(superposition,[],[f13,f54]) ).
fof(f68,plain,
! [X2,X0,X1] : multiply(multiply(X1,inverse(divide(multiply(X1,X2),X0))),X2) = X0,
inference(backward_demodulation,[],[f35,f61]) ).
fof(f71,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(backward_demodulation,[],[f41,f61]) ).
fof(f76,plain,
! [X2,X0,X1] : multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X0)))),X2) = X0,
inference(forward_demodulation,[],[f68,f61]) ).
fof(f94,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f71,f71]) ).
fof(f231,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X1,inverse(inverse(X0))),X2),
inference(superposition,[],[f76,f94]) ).
fof(f252,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X1,X0),X2),
inference(forward_demodulation,[],[f231,f54]) ).
fof(f275,plain,
( multiply(a3,multiply(b3,c3)) != multiply(b3,multiply(a3,c3))
| spl0_1 ),
inference(backward_demodulation,[],[f9,f252]) ).
fof(f285,definition,
( spl0_3
<=> multiply(a3,multiply(b3,c3)) = multiply(b3,multiply(a3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f287,plain,
( multiply(a3,multiply(b3,c3)) != multiply(b3,multiply(a3,c3))
| spl0_3 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,plain,
( ~ spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f275,f7,f285]) ).
fof(f379,plain,
( ! [X0,X1] : multiply(X1,X0) = multiply(X0,multiply(X1,identity))
| ~ spl0_2 ),
inference(superposition,[],[f55,f252]) ).
fof(f380,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f379,f55]) ).
fof(f654,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2)
| ~ spl0_2 ),
inference(superposition,[],[f252,f380]) ).
fof(f662,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f654,f252]) ).
fof(f666,plain,
( $false
| ~ spl0_2
| spl0_3 ),
inference(backward_subsumption_resolution,[],[f287,f662]) ).
fof(f667,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f666]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f20]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f288]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f667]) ).
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(f669,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP535-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 10:09:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 3.43/1.38 % (3311502)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.43/1.38 % (3311536)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=832665528:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.43/1.38 % (3311542)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2595294259:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.43/1.38 % (3311535)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=3243526278:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.43/1.38 % (3311539)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3871813811:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.43/1.38 % (3311533)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=3360824125:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.43/1.38 % (3311541)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4088498953:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.43/1.38 % (3311538)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4169238811:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.43/1.38 % (3311541)First to succeed.
% 3.43/1.38 % (3311539)Also succeeded, but the first one will report.
% 3.43/1.38 % (3311541)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3311502"
% 3.43/1.38 % (3311538)Also succeeded, but the first one will report.
% 3.43/1.38 % (3311541)Refutation found. Thanks to Tanya!
% 3.43/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.43/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.38 % (3311541)------------------------------
% 3.43/1.38 % (3311541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.38 % (3311541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.38 % (3311541)CaDiCaL version: 2.1.3
% 3.43/1.38 % (3311541)Termination reason: Refutation
% 3.43/1.38 % (3311541)Time elapsed: 0.018 s
% 3.43/1.38 % (3311541)Peak memory usage: 89 MB
% 3.43/1.38 % (3311541)Instructions burned: 24 (million)
% 3.43/1.38 % (3311541)------------------------------
% 3.43/1.38 % (3311541)------------------------------
% 3.43/1.38 % (3311502)Success in time 0.411 s
% 3.43/1.38 % Vampire exiting
%------------------------------------------------------------------------------