%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:35:48 AM UTC 2026
% Result : Unsatisfiable 0.21s 1.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 17 unt; 1 def)
% Number of atoms : 17 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f10,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
add(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_plus_a_is_a) ).
fof(f12,plain,
a != add(a,a),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
~ sP0(add(a,a)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f14,plain,
sP0(a),
inference(inequality_splitting,[],[f12,f13]) ).
fof(f31,plain,
! [X0,X1] : add(X0,additive_identity) = multiply(add(X0,X1),add(X0,inverse(X1))),
inference(superposition,[],[f3,f10]) ).
fof(f42,plain,
! [X0,X1] : multiply(add(X0,X1),add(X0,inverse(X1))) = X0,
inference(forward_demodulation,[],[f31,f5]) ).
fof(f134,plain,
! [X0] : multiply(add(X0,X0),multiplicative_identity) = X0,
inference(superposition,[],[f42,f8]) ).
fof(f141,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f134,f6]) ).
fof(f149,plain,
~ sP0(a),
inference(backward_demodulation,[],[f13,f141]) ).
fof(f150,plain,
$false,
inference(forward_subsumption_resolution,[],[f149,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n016.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 21:08:03 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 0.21/1.50 % (4008313)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.21/1.50 % (4008418)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=837535181:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.21/1.50 % (4008420)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3805698941:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.21/1.50 % (4008419)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=701400320:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.21/1.50 % (4008417)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=2284398112:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.21/1.50 % (4008420)First to succeed.
% 0.21/1.50 % (4008420)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4008313"
% 0.21/1.50 % (4008422)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=353924942:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.21/1.50 % (4008421)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3062718929:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.21/1.50 % (4008427)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2425085665:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.21/1.50 % (4008427)Also succeeded, but the first one will report.
% 0.21/1.50 % (4008422)Also succeeded, but the first one will report.
% 0.21/1.50 % (4008421)Also succeeded, but the first one will report.
% 0.21/1.50 % (4008420)Refutation found. Thanks to Tanya!
% 0.21/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.50 % (4008420)------------------------------
% 0.21/1.50 % (4008420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.50 % (4008420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.50 % (4008420)CaDiCaL version: 2.1.3
% 0.21/1.50 % (4008420)Termination reason: Refutation
% 0.21/1.50 % (4008420)Time elapsed: 0.007 s
% 0.21/1.50 % (4008420)Peak memory usage: 88 MB
% 0.21/1.50 % (4008420)Instructions burned: 8 (million)
% 0.21/1.50 % (4008420)------------------------------
% 0.21/1.50 % (4008420)------------------------------
% 0.21/1.50 % (4008313)Success in time 0.585 s
% 0.21/1.50 % Vampire exiting
%------------------------------------------------------------------------------