%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG023-6 : 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 : n018.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 5.99s 2.26s
% Output : Refutation 5.99s
% 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/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f17,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_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/sandbox2/benchmark/theBenchmark.p',associator) ).
fof(f20,negated_conjecture,
associator(x,x,y) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_alternative) ).
fof(f21,plain,
additive_identity != associator(x,x,y),
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
additive_identity != add(multiply(multiply(x,x),y),additive_inverse(multiply(x,multiply(x,y)))),
inference(definition_unfolding,[],[f21,f18]) ).
fof(f23,definition,
~ sP0(add(multiply(multiply(x,x),y),additive_inverse(multiply(x,multiply(x,y))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f24,plain,
sP0(additive_identity),
inference(inequality_splitting,[],[f22,f23]) ).
fof(f25,plain,
~ sP0(add(multiply(x,multiply(x,y)),additive_inverse(multiply(x,multiply(x,y))))),
inference(backward_demodulation,[],[f23,f17]) ).
fof(f26,plain,
~ sP0(additive_identity),
inference(forward_demodulation,[],[f25,f10]) ).
fof(f27,plain,
$false,
inference(forward_subsumption_resolution,[],[f26,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG023-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n018.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 23:01:24 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 5.99/2.26 % (2833524)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.99/2.26 % (2833533)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=651823459:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.99/2.26 % (2833530)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=2058446210:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.99/2.26 % (2833529)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=2266872697:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.99/2.26 % (2833531)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=799771148:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.99/2.26 % (2833532)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2431892196:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.99/2.26 % (2833532)First to succeed.
% 5.99/2.26 % (2833532)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2833524"
% 5.99/2.26 % (2833534)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=164178634:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.99/2.26 % (2833533)Instruction limit reached!
% 5.99/2.26 % (2833533)------------------------------
% 5.99/2.26 % (2833533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/2.26 % (2833533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/2.26 % (2833533)CaDiCaL version: 2.1.3
% 5.99/2.26 % (2833533)Termination reason: Instruction limit
% 5.99/2.26 % (2833533)Termination phase: Saturation
% 5.99/2.26 % (2833533)Time elapsed: 0.089 s
% 5.99/2.26 % (2833533)Peak memory usage: 89 MB
% 5.99/2.26 % (2833533)Instructions burned: 182 (million)
% 5.99/2.26 % (2833535)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1296474405:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.99/2.26 % (2833535)Also succeeded, but the first one will report.
% 5.99/2.26 % (2833534)Also succeeded, but the first one will report.
% 5.99/2.26 % (2833543)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3852704067:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.99/2.26 % (2833532)Refutation found. Thanks to Tanya!
% 5.99/2.26 % SZS status Unsatisfiable for theBenchmark
% 5.99/2.26 % SZS output start Proof for theBenchmark
% See solution above
% 5.99/2.26 % (2833532)------------------------------
% 5.99/2.26 % (2833532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/2.26 % (2833532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/2.26 % (2833532)CaDiCaL version: 2.1.3
% 5.99/2.26 % (2833532)Termination reason: Refutation
% 5.99/2.26 % (2833532)Time elapsed: 0.003 s
% 5.99/2.26 % (2833532)Peak memory usage: 87 MB
% 5.99/2.26 % (2833532)Instructions burned: 1 (million)
% 5.99/2.26 % (2833532)------------------------------
% 5.99/2.26 % (2833532)------------------------------
% 5.99/2.26 % (2833524)Success in time 0.716 s
% 5.99/2.26 % Vampire exiting
%------------------------------------------------------------------------------