%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG018-6 : 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 : n007.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 5.48s 1.97s
% Output : Refutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 24 unt; 1 def)
% Number of atoms : 24 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
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(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(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(f20,negated_conjecture,
multiply(add(x,y),additive_inverse(z)) != add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f21,definition,
~ sP0(multiply(add(x,y),additive_inverse(z))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f22,plain,
sP0(add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z)))),
inference(inequality_splitting,[],[f20,f21]) ).
fof(f23,plain,
~ sP0(add(multiply(x,additive_inverse(z)),multiply(y,additive_inverse(z)))),
inference(backward_demodulation,[],[f21,f13]) ).
fof(f51,plain,
! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
inference(superposition,[],[f15,f8]) ).
fof(f60,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f51,f1]) ).
fof(f69,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f60,f14]) ).
fof(f149,plain,
! [X0,X1] : multiply(X0,additive_identity) = add(multiply(X0,additive_inverse(X1)),multiply(X0,X1)),
inference(superposition,[],[f12,f8]) ).
fof(f170,plain,
! [X0,X1] : additive_identity = add(multiply(X0,additive_inverse(X1)),multiply(X0,X1)),
inference(forward_demodulation,[],[f149,f6]) ).
fof(f375,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = add(additive_inverse(multiply(X0,X1)),additive_identity),
inference(superposition,[],[f69,f170]) ).
fof(f378,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f375,f2]) ).
fof(f402,plain,
~ sP0(add(multiply(x,additive_inverse(z)),additive_inverse(multiply(y,z)))),
inference(backward_demodulation,[],[f23,f378]) ).
fof(f413,plain,
~ sP0(add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z)))),
inference(forward_demodulation,[],[f402,f378]) ).
fof(f424,plain,
$false,
inference(forward_subsumption_resolution,[],[f413,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG018-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 22:56:41 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 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
% 5.48/1.97 % (1870987)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.48/1.97 % (1870993)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=1823448512:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.48/1.97 % (1870995)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1151631010:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.48/1.97 % (1870994)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=775595153:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.48/1.97 % (1870996)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=986954920:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.48/1.97 % (1870998)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2607900824:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.48/1.97 % (1870997)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2034277108:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.48/1.97 % (1870992)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=4105012318:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.48/1.97 % (1870996)Refutation not found, incomplete strategy
% 5.48/1.97 % (1870996)------------------------------
% 5.48/1.97 % (1870996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/1.97 % (1870996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.97 % (1870996)CaDiCaL version: 2.1.3
% 5.48/1.97 % (1870996)Termination reason: Refutation not found, incomplete strategy
% 5.48/1.97 % (1870996)Time elapsed: 0.002 s
% 5.48/1.97 % (1870996)Peak memory usage: 87 MB
% 5.48/1.97 % (1870996)Instructions burned: 1 (million)
% 5.48/1.97 % (1870995)First to succeed.
% 5.48/1.97 % (1870995)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1870987"
% 5.48/1.97 % (1870997)Also succeeded, but the first one will report.
% 5.48/1.97 % (1870998)Also succeeded, but the first one will report.
% 5.48/1.97 % (1870996)------------------------------
% 5.48/1.97 % (1870996)------------------------------
% 5.48/1.97 % (1870995)Refutation found. Thanks to Tanya!
% 5.48/1.97 % SZS status Unsatisfiable for theBenchmark
% 5.48/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 5.48/1.97 % (1870995)------------------------------
% 5.48/1.97 % (1870995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/1.97 % (1870995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.97 % (1870995)CaDiCaL version: 2.1.3
% 5.48/1.97 % (1870995)Termination reason: Refutation
% 5.48/1.97 % (1870995)Time elapsed: 0.017 s
% 5.48/1.97 % (1870995)Peak memory usage: 88 MB
% 5.48/1.97 % (1870995)Instructions burned: 16 (million)
% 5.48/1.97 % (1870995)------------------------------
% 5.48/1.97 % (1870995)------------------------------
% 5.48/1.97 % (1870987)Success in time 0.653 s
% 5.48/1.97 % Vampire exiting
%------------------------------------------------------------------------------