%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG019-6 : 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 12:35:08 PM UTC 2026
% Result : Unsatisfiable 0.32s 2.30s
% Output : Refutation 0.32s
% 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/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
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(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
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(f20,negated_conjecture,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form1) ).
fof(f21,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),
inference(definition_unfolding,[],[f20,f18,f18,f18]) ).
fof(f22,definition,
~ sP0(add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v)))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f23,plain,
sP0(add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))))),
inference(inequality_splitting,[],[f21,f22]) ).
fof(f24,plain,
sP0(add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))))),
inference(backward_demodulation,[],[f23,f15]) ).
fof(f25,plain,
~ sP0(add(add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)),additive_inverse(multiply(x,multiply(y,add(u,v)))))),
inference(backward_demodulation,[],[f22,f12]) ).
fof(f26,plain,
~ sP0(add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,add(u,v))))))),
inference(forward_demodulation,[],[f25,f15]) ).
fof(f27,plain,
~ sP0(add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,add(multiply(y,u),multiply(y,v))))))),
inference(forward_demodulation,[],[f26,f12]) ).
fof(f28,plain,
~ sP0(add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v))))))),
inference(forward_demodulation,[],[f27,f12]) ).
fof(f51,plain,
~ sP0(add(multiply(multiply(x,y),u),add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),multiply(multiply(x,y),v)))),
inference(superposition,[],[f28,f14]) ).
fof(f52,plain,
sP0(add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v))))),
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(x,y),u),additive_inverse(add(multiply(x,multiply(y,u)),additive_inverse(add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v))))))),
inference(backward_demodulation,[],[f52,f689]) ).
fof(f750,plain,
~ sP0(add(multiply(multiply(x,y),u),additive_inverse(add(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v))),additive_inverse(multiply(multiply(x,y),v)))))),
inference(backward_demodulation,[],[f51,f689]) ).
fof(f770,plain,
~ sP0(add(multiply(multiply(x,y),u),additive_inverse(add(multiply(x,multiply(y,u)),add(multiply(x,multiply(y,v)),additive_inverse(multiply(multiply(x,y),v))))))),
inference(forward_demodulation,[],[f750,f15]) ).
fof(f776,plain,
sP0(add(multiply(multiply(x,y),u),additive_inverse(add(multiply(x,multiply(y,u)),additive_inverse(additive_inverse(add(multiply(x,multiply(y,v)),additive_inverse(multiply(multiply(x,y),v))))))))),
inference(forward_demodulation,[],[f743,f689]) ).
fof(f803,plain,
sP0(add(multiply(multiply(x,y),u),additive_inverse(add(multiply(x,multiply(y,u)),add(multiply(x,multiply(y,v)),additive_inverse(multiply(multiply(x,y),v))))))),
inference(forward_demodulation,[],[f776,f11]) ).
fof(f819,plain,
$false,
inference(forward_subsumption_resolution,[],[f803,f770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG019-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.50 % Computer : n018.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Sun Sep 27 23:00:54 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.56 Running first-order theorem proving
% 0.28/0.57 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
% 0.32/2.30 % (2832666)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.32/2.30 % (2832671)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=2508121232:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.32/2.30 % (2832673)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2368246380:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.32/2.30 % (2832674)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2729415513:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.32/2.30 % (2832672)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=3349214561:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.32/2.30 % (2832676)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=96449123:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.32/2.30 % (2832677)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=301737228:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.32/2.30 % (2832675)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3403584559:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.32/2.30 % (2832674)First to succeed.
% 0.32/2.30 % (2832674)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2832666"
% 0.32/2.30 % (2832676)Also succeeded, but the first one will report.
% 0.32/2.30 % (2832675)Instruction limit reached!
% 0.32/2.30 % (2832675)------------------------------
% 0.32/2.30 % (2832675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.30 % (2832675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.30 % (2832675)CaDiCaL version: 2.1.3
% 0.32/2.30 % (2832675)Termination reason: Instruction limit
% 0.32/2.30 % (2832675)Termination phase: Saturation
% 0.32/2.30 % (2832675)Time elapsed: 0.174 s
% 0.32/2.30 % (2832675)Peak memory usage: 89 MB
% 0.32/2.30 % (2832675)Instructions burned: 181 (million)
% 0.32/2.30 % (2832674)Refutation found. Thanks to Tanya!
% 0.32/2.30 % SZS status Unsatisfiable for theBenchmark
% 0.32/2.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.32/2.31 % (2832674)------------------------------
% 0.32/2.31 % (2832674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.31 % (2832674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.31 % (2832674)CaDiCaL version: 2.1.3
% 0.32/2.31 % (2832674)Termination reason: Refutation
% 0.32/2.31 % (2832674)Time elapsed: 0.033 s
% 0.32/2.31 % (2832674)Peak memory usage: 88 MB
% 0.32/2.31 % (2832674)Instructions burned: 31 (million)
% 0.32/2.31 % (2832674)------------------------------
% 0.32/2.31 % (2832674)------------------------------
% 0.32/2.31 % (2832666)Success in time 0.732 s
% 0.32/2.31 % Vampire exiting
%------------------------------------------------------------------------------