%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO005-4 : 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 : n001.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 09:35:49 AM UTC 2026
% Result : Unsatisfiable 6.18s 1.96s
% Output : Refutation 6.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 32 unt; 3 def)
% Number of atoms : 64 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 15 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 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(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/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/sandbox2/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,multiplicative_identity) != multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_plus_1_is_a) ).
fof(f12,plain,
multiplicative_identity != add(a,multiplicative_identity),
inference(reorient_equations,[],[f11]) ).
fof(f14,definition,
( spl0_1
<=> multiplicative_identity = add(a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f16,plain,
( multiplicative_identity != add(a,multiplicative_identity)
| spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f12,f14]) ).
fof(f18,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(add(multiply(X0,X1),X0),add(multiply(X0,X1),X2)),
inference(backward_demodulation,[],[f4,f3]) ).
fof(f22,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f5,f1]) ).
fof(f30,plain,
multiplicative_identity = inverse(additive_identity),
inference(superposition,[],[f8,f22]) ).
fof(f34,definition,
( spl0_2
<=> multiplicative_identity = inverse(additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f36,plain,
( multiplicative_identity = inverse(additive_identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
spl0_2,
inference(avatar_split_clause,[],[f30,f34]) ).
fof(f39,plain,
( inverse(additive_identity) != add(a,inverse(additive_identity))
| spl0_1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f16,f36]) ).
fof(f40,plain,
( ! [X0] : multiply(X0,inverse(additive_identity)) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f6,f36]) ).
fof(f43,definition,
( spl0_3
<=> inverse(additive_identity) = add(a,inverse(additive_identity)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f45,plain,
( inverse(additive_identity) != add(a,inverse(additive_identity))
| spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( ~ spl0_3
| spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f39,f34,f14,f43]) ).
fof(f54,plain,
! [X2,X0,X1] : multiply(add(X0,X1),add(X0,X2)) = add(multiply(X1,X2),X0),
inference(superposition,[],[f1,f3]) ).
fof(f78,plain,
! [X0,X1] : multiply(add(additive_identity,X0),add(additive_identity,X1)) = multiply(X0,add(inverse(X0),X1)),
inference(superposition,[],[f18,f10]) ).
fof(f97,plain,
! [X0,X1] : multiply(add(additive_identity,X0),X1) = multiply(X0,add(inverse(X0),X1)),
inference(forward_demodulation,[],[f78,f22]) ).
fof(f100,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(inverse(X0),X1)),
inference(forward_demodulation,[],[f97,f22]) ).
fof(f118,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(superposition,[],[f100,f5]) ).
fof(f133,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[],[f118,f10]) ).
fof(f139,plain,
! [X0,X1] : add(multiply(X1,additive_identity),X0) = multiply(add(X0,X1),X0),
inference(superposition,[],[f54,f5]) ).
fof(f191,plain,
! [X0,X1] : add(additive_identity,X0) = multiply(add(X0,X1),X0),
inference(forward_demodulation,[],[f139,f133]) ).
fof(f195,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f191,f22]) ).
fof(f228,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(superposition,[],[f195,f1]) ).
fof(f384,plain,
( ! [X0] : inverse(additive_identity) = add(X0,inverse(additive_identity))
| ~ spl0_2 ),
inference(superposition,[],[f40,f228]) ).
fof(f385,plain,
( $false
| ~ spl0_2
| spl0_3 ),
inference(backward_subsumption_resolution,[],[f45,f384]) ).
fof(f388,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f385]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f37]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f388]) ).
cnf(s8,plain,
spl0_3,
inference(rat,[],[s7,s2]) ).
cnf(s9,plain,
spl0_1,
inference(rat,[],[s4,s8,s2]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9]) ).
fof(f390,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n001.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Mon Sep 28 21:09:19 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running first-order theorem proving
% 0.24/0.31 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
% 6.18/1.96 % (748410)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.18/1.96 % (748417)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3722913894:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.18/1.96 % (748416)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=3567353113:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.18/1.96 % (748420)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3932755026:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.18/1.96 % (748415)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=3992637215:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.18/1.96 % (748420)First to succeed.
% 6.18/1.96 % (748420)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-748410"
% 6.18/1.96 % (748419)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3884790737:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.18/1.96 % (748418)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3333046414:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.18/1.96 % (748418)Also succeeded, but the first one will report.
% 6.18/1.96 % (748419)Also succeeded, but the first one will report.
% 6.18/1.96 % (748421)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1690792617:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.18/1.96 % (748421)Also succeeded, but the first one will report.
% 6.18/1.96 % (748420)Refutation found. Thanks to Tanya!
% 6.18/1.96 % SZS status Unsatisfiable for theBenchmark
% 6.18/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 6.18/1.96 % (748420)------------------------------
% 6.18/1.96 % (748420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.18/1.96 % (748420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.18/1.96 % (748420)CaDiCaL version: 2.1.3
% 6.18/1.96 % (748420)Termination reason: Refutation
% 6.18/1.96 % (748420)Time elapsed: 0.030 s
% 6.18/1.96 % (748420)Peak memory usage: 89 MB
% 6.18/1.96 % (748420)Instructions burned: 24 (million)
% 6.18/1.96 % (748420)------------------------------
% 6.18/1.96 % (748420)------------------------------
% 6.18/1.96 % (748410)Success in time 0.734 s
% 6.18/1.96 % Vampire exiting
%------------------------------------------------------------------------------