%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:35:52 AM UTC 2026
% Result : Unsatisfiable 3.99s 1.57s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id2) ).
fof(f15,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
fof(f17,axiom,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_and_multiplicative_identity) ).
fof(f18,plain,
multiplicative_identity = add(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
add(a,c) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_and_multiplicative_identity) ).
fof(f20,plain,
multiplicative_identity = add(a,c),
inference(reorient_equations,[],[f19]) ).
fof(f21,axiom,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_a_additive_identity) ).
fof(f22,plain,
additive_identity = multiply(a,b),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
multiply(a,c) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_a_additive_identity) ).
fof(f24,plain,
additive_identity = multiply(a,c),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_a) ).
fof(f72,plain,
! [X0] : add(multiply(a,X0),b) = multiply(multiplicative_identity,add(X0,b)),
inference(superposition,[],[f3,f18]) ).
fof(f73,plain,
! [X0] : add(multiply(a,X0),c) = multiply(multiplicative_identity,add(X0,c)),
inference(superposition,[],[f3,f20]) ).
fof(f92,plain,
! [X0] : add(multiply(a,X0),c) = add(X0,c),
inference(forward_demodulation,[],[f73,f14]) ).
fof(f93,plain,
! [X0] : add(multiply(a,X0),b) = add(X0,b),
inference(forward_demodulation,[],[f72,f14]) ).
fof(f101,plain,
! [X0] : add(X0,c) = add(c,multiply(a,X0)),
inference(forward_demodulation,[],[f92,f1]) ).
fof(f102,plain,
! [X0] : add(X0,b) = add(b,multiply(a,X0)),
inference(forward_demodulation,[],[f93,f1]) ).
fof(f204,plain,
add(c,additive_identity) = add(b,c),
inference(superposition,[],[f101,f22]) ).
fof(f218,plain,
c = add(b,c),
inference(forward_demodulation,[],[f204,f15]) ).
fof(f238,plain,
add(b,additive_identity) = add(c,b),
inference(superposition,[],[f102,f24]) ).
fof(f250,plain,
add(b,additive_identity) = add(b,c),
inference(forward_demodulation,[],[f238,f1]) ).
fof(f254,plain,
c = add(b,additive_identity),
inference(forward_demodulation,[],[f250,f218]) ).
fof(f255,plain,
b = c,
inference(forward_demodulation,[],[f254,f15]) ).
fof(f256,plain,
$false,
inference(forward_subsumption_resolution,[],[f255,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n003.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Mon Sep 28 21:05:43 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.29 Running first-order theorem proving
% 0.10/0.29 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
% 3.99/1.57 % (2017813)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.99/1.57 % (2017829)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1123382751:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.99/1.57 % (2017833)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4055844371:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.99/1.57 % (2017833)First to succeed.
% 3.99/1.57 % (2017833)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2017813"
% 3.99/1.57 % (2017828)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=668164005:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.99/1.57 % (2017827)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=1447694315:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.99/1.57 % (2017831)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2725352923:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.99/1.57 % (2017830)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1433501372:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.99/1.57 % (2017832)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2473284181:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.99/1.57 % (2017830)Also succeeded, but the first one will report.
% 3.99/1.57 % (2017831)Instruction limit reached!
% 3.99/1.57 % (2017831)------------------------------
% 3.99/1.57 % (2017831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.57 % (2017831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.57 % (2017831)CaDiCaL version: 2.1.3
% 3.99/1.57 % (2017831)Termination reason: Instruction limit
% 3.99/1.57 % (2017831)Termination phase: Saturation
% 3.99/1.57 % (2017831)Time elapsed: 0.183 s
% 3.99/1.57 % (2017831)Peak memory usage: 89 MB
% 3.99/1.57 % (2017831)Instructions burned: 181 (million)
% 3.99/1.57 % (2017833)Refutation found. Thanks to Tanya!
% 3.99/1.57 % SZS status Unsatisfiable for theBenchmark
% 3.99/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/1.57 % (2017833)------------------------------
% 3.99/1.57 % (2017833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.57 % (2017833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.57 % (2017833)CaDiCaL version: 2.1.3
% 3.99/1.57 % (2017833)Termination reason: Refutation
% 3.99/1.57 % (2017833)Time elapsed: 0.006 s
% 3.99/1.57 % (2017833)Peak memory usage: 88 MB
% 3.99/1.57 % (2017833)Instructions burned: 9 (million)
% 3.99/1.57 % (2017833)------------------------------
% 3.99/1.57 % (2017833)------------------------------
% 3.99/1.57 % (2017813)Success in time 0.437 s
% 3.99/1.57 % Vampire exiting
%------------------------------------------------------------------------------