%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG021-7 : 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 : n005.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 3.01s 1.25s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 23 unt; 1 def)
% Number of atoms : 23 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
fof(f25,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(reorient_equations,[],[f24]) ).
fof(f29,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),additive_inverse(X2)) = add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference4) ).
fof(f30,negated_conjecture,
associator(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form3) ).
fof(f31,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,[],[f30,f18,f18,f18]) ).
fof(f32,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(f33,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,[],[f31,f32]) ).
fof(f34,plain,
! [X2,X0,X1] : add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X1,X2))) = additive_inverse(multiply(add(X0,X1),X2)),
inference(backward_demodulation,[],[f29,f25]) ).
fof(f37,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,[],[f33,f15]) ).
fof(f38,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,[],[f32,f13]) ).
fof(f41,plain,
! [X2,X0,X1] : add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X1,X2))) = additive_inverse(add(multiply(X0,X2),multiply(X1,X2))),
inference(forward_demodulation,[],[f34,f13]) ).
fof(f44,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,[],[f38,f13]) ).
fof(f45,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,[],[f44,f13]) ).
fof(f46,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,[],[f45,f15]) ).
fof(f69,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,[],[f46,f14]) ).
fof(f70,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,[],[f37,f14]) ).
fof(f518,plain,
! [X2,X3,X0,X1] : add(additive_inverse(multiply(X0,X1)),add(additive_inverse(multiply(X2,X1)),X3)) = add(additive_inverse(add(multiply(X0,X1),multiply(X2,X1))),X3),
inference(superposition,[],[f15,f41]) ).
fof(f525,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(backward_demodulation,[],[f69,f518]) ).
fof(f540,plain,
$false,
inference(forward_subsumption_resolution,[],[f525,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG021-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:59:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.01/1.25 % (278358)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.01/1.25 % (278366)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1494855994:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.01/1.25 % (278366)First to succeed.
% 3.01/1.25 % (278366)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-278358"
% 3.01/1.25 % (278364)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=931408002:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.01/1.25 % (278367)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3194412791:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.01/1.25 % (278367)Refutation not found, incomplete strategy
% 3.01/1.25 % (278367)------------------------------
% 3.01/1.25 % (278367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.25 % (278367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.25 % (278367)CaDiCaL version: 2.1.3
% 3.01/1.25 % (278367)Termination reason: Refutation not found, incomplete strategy
% 3.01/1.25 % (278367)Time elapsed: 0.004 s
% 3.01/1.25 % (278367)Peak memory usage: 88 MB
% 3.01/1.25 % (278367)Instructions burned: 2 (million)
% 3.01/1.25 % (278369)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=936849436:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.01/1.25 % (278363)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=2915049045:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.01/1.25 % (278365)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=481307612:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.01/1.25 % (278368)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=733025654:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.01/1.25 % (278368)Also succeeded, but the first one will report.
% 3.01/1.25 % (278366)Refutation found. Thanks to Tanya!
% 3.01/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.01/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.01/1.25 % (278366)------------------------------
% 3.01/1.25 % (278366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.25 % (278366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.25 % (278366)CaDiCaL version: 2.1.3
% 3.01/1.25 % (278366)Termination reason: Refutation
% 3.01/1.25 % (278366)Time elapsed: 0.007 s
% 3.01/1.25 % (278366)Peak memory usage: 88 MB
% 3.01/1.25 % (278366)Instructions burned: 20 (million)
% 3.01/1.25 % (278366)------------------------------
% 3.01/1.25 % (278366)------------------------------
% 3.01/1.25 % (278358)Success in time 0.404 s
% 3.01/1.25 % Vampire exiting
%------------------------------------------------------------------------------