%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG016-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:35:08 PM UTC 2026
% Result : Unsatisfiable 2.58s 1.34s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 29 unt; 3 def)
% Number of atoms : 61 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 14 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
fof(f3,axiom,
! [X0] : multiply(additive_identity,X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
fof(f4,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(reorient_equations,[],[f3]) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
fof(f8,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f20,negated_conjecture,
multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f22,definition,
( spl0_1
<=> multiply(add(x,additive_inverse(y)),z) = add(multiply(x,z),additive_inverse(multiply(y,z))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f24,plain,
( multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z)))
| spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f20,f22]) ).
fof(f26,plain,
( add(multiply(x,z),additive_inverse(multiply(y,z))) != add(multiply(x,z),multiply(additive_inverse(y),z))
| spl0_1 ),
inference(forward_demodulation,[],[f24,f13]) ).
fof(f28,definition,
( spl0_2
<=> add(multiply(x,z),additive_inverse(multiply(y,z))) = add(multiply(x,z),multiply(additive_inverse(y),z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f30,plain,
( add(multiply(x,z),additive_inverse(multiply(y,z))) != add(multiply(x,z),multiply(additive_inverse(y),z))
| spl0_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f26,f22,f28]) ).
fof(f34,plain,
additive_identity = additive_inverse(additive_identity),
inference(superposition,[],[f2,f8]) ).
fof(f36,definition,
( spl0_3
<=> additive_identity = additive_inverse(additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f38,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,plain,
spl0_3,
inference(avatar_split_clause,[],[f34,f36]) ).
fof(f64,plain,
! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
inference(superposition,[],[f15,f8]) ).
fof(f73,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f64,f1]) ).
fof(f93,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f73,f14]) ).
fof(f131,plain,
! [X0,X1] : additive_inverse(X1) = add(additive_inverse(add(X1,X0)),X0),
inference(superposition,[],[f93,f73]) ).
fof(f202,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(superposition,[],[f14,f131]) ).
fof(f490,plain,
! [X0,X1] : multiply(additive_identity,X1) = add(multiply(X0,X1),multiply(additive_inverse(X0),X1)),
inference(superposition,[],[f13,f10]) ).
fof(f509,plain,
! [X0,X1] : additive_identity = add(multiply(X0,X1),multiply(additive_inverse(X0),X1)),
inference(forward_demodulation,[],[f490,f4]) ).
fof(f636,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = add(multiply(additive_inverse(X0),X1),additive_inverse(additive_identity)),
inference(superposition,[],[f202,f509]) ).
fof(f639,plain,
( ! [X0,X1] : additive_inverse(multiply(X0,X1)) = add(multiply(additive_inverse(X0),X1),additive_identity)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f636,f38]) ).
fof(f653,plain,
( ! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f639,f2]) ).
fof(f672,plain,
( add(multiply(x,z),additive_inverse(multiply(y,z))) != add(multiply(x,z),additive_inverse(multiply(y,z)))
| spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[],[f30,f653]) ).
fof(f673,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f672]) ).
fof(f674,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f673]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f39]) ).
cnf(s5,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f674]) ).
cnf(s6,plain,
spl0_2,
inference(rat,[],[s5,s3]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s2,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f706,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG016-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 23:02:02 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.58/1.34 % (2112895)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.58/1.34 % (2112990)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=233108223:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.58/1.34 % (2112990)First to succeed.
% 2.58/1.34 % (2112990)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2112895"
% 2.58/1.34 % (2112988)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1242123586:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.58/1.34 % (2112984)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=3907492309:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.58/1.34 % (2112989)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=819160563:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.58/1.34 % (2112987)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=968915889:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.58/1.34 % (2112989)Refutation not found, incomplete strategy
% 2.58/1.34 % (2112989)------------------------------
% 2.58/1.34 % (2112989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.34 % (2112989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.34 % (2112989)CaDiCaL version: 2.1.3
% 2.58/1.34 % (2112989)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.34 % (2112989)Time elapsed: 0.001 s
% 2.58/1.34 % (2112989)Peak memory usage: 87 MB
% 2.58/1.34 % (2112989)Instructions burned: 1 (million)
% 2.58/1.34 % (2112985)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=806764034:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.58/1.34 % (2112988)Also succeeded, but the first one will report.
% 2.58/1.34 % (2112991)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3648673009:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.58/1.34 % (2112990)Refutation found. Thanks to Tanya!
% 2.58/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.34 % (2112990)------------------------------
% 2.58/1.34 % (2112990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.34 % (2112990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.34 % (2112990)CaDiCaL version: 2.1.3
% 2.58/1.34 % (2112990)Termination reason: Refutation
% 2.58/1.34 % (2112990)Time elapsed: 0.010 s
% 2.58/1.34 % (2112990)Peak memory usage: 89 MB
% 2.58/1.34 % (2112990)Instructions burned: 25 (million)
% 2.58/1.34 % (2112990)------------------------------
% 2.58/1.34 % (2112990)------------------------------
% 2.58/1.34 % (2112895)Success in time 0.293 s
% 2.58/1.34 % Vampire exiting
%------------------------------------------------------------------------------