%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG021-6 : 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 : n010.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 5.89s 1.94s
% Output : Refutation 5.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 35 unt; 1 def)
% Number of atoms : 35 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
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(f20,negated_conjecture,
associator(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_linearised_form3) ).
fof(f21,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(add(multiply(multiply(u,x),y),additive_inverse(multiply(u,multiply(x,y)))),add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y))))),
inference(definition_unfolding,[],[f20,f18,f18,f18]) ).
fof(f22,definition,
~ sP0(add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f23,plain,
sP0(add(add(multiply(multiply(u,x),y),additive_inverse(multiply(u,multiply(x,y)))),add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y)))))),
inference(inequality_splitting,[],[f21,f22]) ).
fof(f24,plain,
sP0(add(multiply(multiply(u,x),y),add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y))))))),
inference(backward_demodulation,[],[f23,f15]) ).
fof(f25,plain,
~ sP0(add(multiply(multiply(add(u,v),x),y),additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y)))))),
inference(backward_demodulation,[],[f22,f13]) ).
fof(f26,plain,
~ sP0(add(multiply(add(multiply(u,x),multiply(v,x)),y),additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y)))))),
inference(forward_demodulation,[],[f25,f13]) ).
fof(f27,plain,
~ sP0(add(add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)),additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y)))))),
inference(forward_demodulation,[],[f26,f13]) ).
fof(f28,plain,
~ sP0(add(multiply(multiply(u,x),y),add(multiply(multiply(v,x),y),additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y))))))),
inference(forward_demodulation,[],[f27,f15]) ).
fof(f51,plain,
~ sP0(add(multiply(multiply(u,x),y),add(additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y)))),multiply(multiply(v,x),y)))),
inference(superposition,[],[f28,f14]) ).
fof(f52,plain,
sP0(add(multiply(multiply(u,x),y),add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(v,x),y))))),
inference(superposition,[],[f24,f14]) ).
fof(f55,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
inference(superposition,[],[f15,f10]) ).
fof(f60,plain,
! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
inference(superposition,[],[f15,f8]) ).
fof(f69,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f60,f1]) ).
fof(f71,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f55,f1]) ).
fof(f100,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f69,f14]) ).
fof(f200,plain,
! [X0,X1] : add(X1,add(X0,additive_inverse(X1))) = X0,
inference(superposition,[],[f71,f14]) ).
fof(f283,plain,
! [X0,X1] : additive_inverse(X1) = add(additive_inverse(add(X0,X1)),X0),
inference(superposition,[],[f100,f100]) ).
fof(f689,plain,
! [X0,X1] : add(additive_inverse(X0),X1) = additive_inverse(add(X0,additive_inverse(X1))),
inference(superposition,[],[f283,f200]) ).
fof(f743,plain,
sP0(add(multiply(multiply(u,x),y),additive_inverse(add(multiply(u,multiply(x,y)),additive_inverse(add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(v,x),y))))))),
inference(backward_demodulation,[],[f52,f689]) ).
fof(f750,plain,
~ sP0(add(multiply(multiply(u,x),y),additive_inverse(add(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y))),additive_inverse(multiply(multiply(v,x),y)))))),
inference(backward_demodulation,[],[f51,f689]) ).
fof(f770,plain,
~ sP0(add(multiply(multiply(u,x),y),additive_inverse(add(multiply(u,multiply(x,y)),add(multiply(v,multiply(x,y)),additive_inverse(multiply(multiply(v,x),y))))))),
inference(forward_demodulation,[],[f750,f15]) ).
fof(f776,plain,
sP0(add(multiply(multiply(u,x),y),additive_inverse(add(multiply(u,multiply(x,y)),additive_inverse(additive_inverse(add(multiply(v,multiply(x,y)),additive_inverse(multiply(multiply(v,x),y))))))))),
inference(forward_demodulation,[],[f743,f689]) ).
fof(f803,plain,
sP0(add(multiply(multiply(u,x),y),additive_inverse(add(multiply(u,multiply(x,y)),add(multiply(v,multiply(x,y)),additive_inverse(multiply(multiply(v,x),y))))))),
inference(forward_demodulation,[],[f776,f11]) ).
fof(f819,plain,
$false,
inference(forward_subsumption_resolution,[],[f803,f770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG021-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n010.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 22:59:32 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 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
% 5.89/1.94 % (1401507)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.89/1.94 % (1401520)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=604728130:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.89/1.94 % (1401519)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1317452479:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.89/1.94 % (1401515)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=3891354913:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.89/1.94 % (1401516)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3125255638:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.89/1.94 % (1401517)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2595068166:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.89/1.94 % (1401518)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2780059782:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.89/1.94 % (1401514)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=3220824530:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.89/1.94 % (1401517)First to succeed.
% 5.89/1.94 % (1401517)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1401507"
% 5.89/1.94 % (1401519)Also succeeded, but the first one will report.
% 5.89/1.94 % (1401518)Instruction limit reached!
% 5.89/1.94 % (1401518)------------------------------
% 5.89/1.94 % (1401518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.94 % (1401518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.94 % (1401518)CaDiCaL version: 2.1.3
% 5.89/1.94 % (1401518)Termination reason: Instruction limit
% 5.89/1.94 % (1401518)Termination phase: Saturation
% 5.89/1.94 % (1401518)Time elapsed: 0.171 s
% 5.89/1.94 % (1401518)Peak memory usage: 89 MB
% 5.89/1.94 % (1401518)Instructions burned: 181 (million)
% 5.89/1.94 % (1401528)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2077981627:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 5.89/1.94 % (1401517)Refutation found. Thanks to Tanya!
% 5.89/1.94 % SZS status Unsatisfiable for theBenchmark
% 5.89/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 5.89/1.94 % (1401517)------------------------------
% 5.89/1.94 % (1401517)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.94 % (1401517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.94 % (1401517)CaDiCaL version: 2.1.3
% 5.89/1.94 % (1401517)Termination reason: Refutation
% 5.89/1.94 % (1401517)Time elapsed: 0.032 s
% 5.89/1.94 % (1401517)Peak memory usage: 88 MB
% 5.89/1.94 % (1401517)Instructions burned: 31 (million)
% 5.89/1.94 % (1401517)------------------------------
% 5.89/1.94 % (1401517)------------------------------
% 5.89/1.94 % (1401507)Success in time 0.719 s
% 5.89/1.94 % Vampire exiting
%------------------------------------------------------------------------------