%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:35:09 PM UTC 2026
% Result : Unsatisfiable 3.47s 1.43s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 12 unt; 1 def)
% Number of atoms : 12 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f16,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_alternative) ).
fof(f18,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
fof(f30,negated_conjecture,
associator(x,y,y) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_alternative) ).
fof(f31,plain,
additive_identity != associator(x,y,y),
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
additive_identity != add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))),
inference(definition_unfolding,[],[f31,f18]) ).
fof(f33,definition,
~ sP0(add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f34,plain,
sP0(additive_identity),
inference(inequality_splitting,[],[f32,f33]) ).
fof(f38,plain,
~ sP0(add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y))))),
inference(backward_demodulation,[],[f33,f16]) ).
fof(f44,plain,
~ sP0(additive_identity),
inference(forward_demodulation,[],[f38,f10]) ).
fof(f45,plain,
$false,
inference(forward_subsumption_resolution,[],[f44,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:01:12 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.47/1.43 % (1026287)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.47/1.43 % (1026348)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=2746066128:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.47/1.43 % (1026349)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=1122348650:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.47/1.43 % (1026351)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=727084333:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.47/1.43 % (1026350)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=463794666:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.47/1.43 % (1026351)First to succeed.
% 3.47/1.43 % (1026351)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1026287"
% 3.47/1.43 % (1026353)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1484543792:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.47/1.43 % (1026352)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3925795989:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.47/1.43 % (1026352)Refutation not found, incomplete strategy
% 3.47/1.43 % (1026352)------------------------------
% 3.47/1.43 % (1026352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.43 % (1026352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.43 % (1026352)CaDiCaL version: 2.1.3
% 3.47/1.43 % (1026352)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.43 % (1026352)Time elapsed: 0.002 s
% 3.47/1.43 % (1026352)Peak memory usage: 87 MB
% 3.47/1.43 % (1026352)Instructions burned: 1 (million)
% 3.47/1.43 % (1026353)Also succeeded, but the first one will report.
% 3.47/1.43 % (1026354)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2605319874:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.47/1.43 % (1026354)Also succeeded, but the first one will report.
% 3.47/1.43 % (1026351)Refutation found. Thanks to Tanya!
% 3.47/1.43 % SZS status Unsatisfiable for theBenchmark
% 3.47/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.43 % (1026351)------------------------------
% 3.47/1.43 % (1026351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.43 % (1026351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.43 % (1026351)CaDiCaL version: 2.1.3
% 3.47/1.43 % (1026351)Termination reason: Refutation
% 3.47/1.43 % (1026351)Time elapsed: 0.002 s
% 3.47/1.43 % (1026351)Peak memory usage: 87 MB
% 3.47/1.43 % (1026351)Instructions burned: 2 (million)
% 3.47/1.43 % (1026351)------------------------------
% 3.47/1.43 % (1026351)------------------------------
% 3.47/1.43 % (1026287)Success in time 0.43 s
% 3.47/1.43 % Vampire exiting
%------------------------------------------------------------------------------