%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 10:13:15 AM UTC 2026
% Result : Unsatisfiable 0.94s 1.22s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 35 unt; 4 def)
% Number of atoms : 87 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 22 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f17,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22a) ).
fof(f18,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(reorient_equations,[],[f17]) ).
fof(f20,definition,
( spl0_1
<=> multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))
| spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f18,f20]) ).
fof(f24,plain,
( multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))))
| spl0_1 ),
inference(forward_demodulation,[],[f22,f8]) ).
fof(f25,plain,
( least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),multiply(identity,least_upper_bound(b,identity)))))
| spl0_1 ),
inference(forward_demodulation,[],[f24,f15]) ).
fof(f26,plain,
( least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),multiply(identity,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),multiply(identity,identity)))))
| spl0_1 ),
inference(forward_demodulation,[],[f25,f13]) ).
fof(f27,plain,
( least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),identity)) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(multiply(identity,b),identity))))
| spl0_1 ),
inference(forward_demodulation,[],[f26,f1]) ).
fof(f28,plain,
( least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(b,identity)) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,least_upper_bound(b,identity)),least_upper_bound(b,identity))))
| spl0_1 ),
inference(forward_demodulation,[],[f27,f1]) ).
fof(f29,plain,
( least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),least_upper_bound(b,identity)) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(least_upper_bound(multiply(a,b),multiply(a,identity)),least_upper_bound(b,identity))))
| spl0_1 ),
inference(forward_demodulation,[],[f28,f13]) ).
fof(f30,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity)))))
| spl0_1 ),
inference(forward_demodulation,[],[f29,f8]) ).
fof(f32,definition,
( spl0_2
<=> least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity))))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f34,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(multiply(a,identity),least_upper_bound(b,identity)))))
| spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f30,f20,f32]) ).
fof(f47,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f56,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),X0),
inference(superposition,[],[f47,f12]) ).
fof(f58,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,X0)),
inference(forward_demodulation,[],[f56,f8]) ).
fof(f60,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f63,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f60,f1]) ).
fof(f76,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f63,f3]) ).
fof(f78,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f63,f63]) ).
fof(f81,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f76,f78]) ).
fof(f83,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity)))))
| spl0_2 ),
inference(backward_demodulation,[],[f34,f81]) ).
fof(f85,definition,
( spl0_4
<=> least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f87,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity)))))
| spl0_4 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( ~ spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f83,f32,f85]) ).
fof(f186,plain,
! [X2,X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(least_upper_bound(X1,X0),X2)),
inference(superposition,[],[f8,f58]) ).
fof(f195,plain,
! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))),
inference(superposition,[],[f58,f8]) ).
fof(f199,plain,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1)),
inference(superposition,[],[f6,f8]) ).
fof(f208,plain,
! [X2,X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))),
inference(forward_demodulation,[],[f186,f8]) ).
fof(f214,plain,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))),
inference(forward_demodulation,[],[f208,f8]) ).
fof(f215,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,identity))))
| spl0_4 ),
inference(backward_demodulation,[],[f87,f214]) ).
fof(f218,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,b)))
| spl0_4 ),
inference(forward_demodulation,[],[f215,f195]) ).
fof(f225,definition,
( spl0_8
<=> least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) = least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,b))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f227,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,b)))
| spl0_8 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,plain,
( ~ spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f218,f85,f225]) ).
fof(f1700,plain,
( least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),least_upper_bound(a,least_upper_bound(b,identity)))
| spl0_8 ),
inference(superposition,[],[f227,f199]) ).
fof(f1708,plain,
( $false
| spl0_8 ),
inference(trivial_inequality_removal,[],[f1700]) ).
fof(f1709,plain,
spl0_8,
inference(avatar_contradiction_clause,[],[f1708]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s5,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f88]) ).
cnf(s10,plain,
( spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f228]) ).
cnf(s21,plain,
spl0_8,
inference(sat_conversion,[],[f1709]) ).
cnf(s36,plain,
spl0_4,
inference(rat,[],[s10,s21]) ).
cnf(s39,plain,
spl0_2,
inference(rat,[],[s5,s36]) ).
cnf(s40,plain,
spl0_1,
inference(rat,[],[s2,s39]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s1,s40]) ).
fof(f1832,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n009.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 09:36:30 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 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
% 0.94/1.22 % (1777305)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.94/1.22 % (1777315)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4168373332:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 0.94/1.22 % (1777315)First to succeed.
% 0.94/1.22 % (1777315)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1777305"
% 0.94/1.22 % (1777314)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1772185848:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 0.94/1.22 % (1777313)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1934095305:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 0.94/1.22 % (1777311)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=1635718408:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 0.94/1.22 % (1777312)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=581739232:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 0.94/1.22 % (1777316)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2995739242:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 0.94/1.22 % (1777310)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=67949135:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 0.94/1.22 % (1777313)Also succeeded, but the first one will report.
% 0.94/1.22 % (1777315)Refutation found. Thanks to Tanya!
% 0.94/1.22 % SZS status Unsatisfiable for theBenchmark
% 0.94/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.38 % (1777315)------------------------------
% 3.35/1.38 % (1777315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.38 % (1777315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.38 % (1777315)CaDiCaL version: 2.1.3
% 3.35/1.38 % (1777315)Termination reason: Refutation
% 3.35/1.38 % (1777315)Time elapsed: 0.033 s
% 3.35/1.38 % (1777315)Peak memory usage: 89 MB
% 3.35/1.38 % (1777315)Instructions burned: 60 (million)
% 3.35/1.38 % (1777315)------------------------------
% 3.35/1.38 % (1777315)------------------------------
% 3.35/1.38 % (1777305)Success in time 0.402 s
% 3.35/1.38 % Vampire exiting
%------------------------------------------------------------------------------