%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO009-4 : 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 : n017.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 09:35:51 AM UTC 2026
% Result : Unsatisfiable 3.58s 1.26s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 34 unt; 4 def)
% Number of atoms : 70 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 14 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
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(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
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,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_operation) ).
fof(f12,plain,
a != multiply(a,add(a,b)),
inference(reorient_equations,[],[f11]) ).
fof(f14,definition,
( spl0_1
<=> a = multiply(a,add(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f16,plain,
( a != multiply(a,add(a,b))
| spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f12,f14]) ).
fof(f18,plain,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = add(multiply(add(X0,X1),X0),multiply(add(X0,X1),X2)),
inference(forward_demodulation,[],[f3,f4]) ).
fof(f19,plain,
( a != add(multiply(a,a),multiply(a,b))
| spl0_1 ),
inference(forward_demodulation,[],[f16,f4]) ).
fof(f21,definition,
( spl0_2
<=> a = add(multiply(a,a),multiply(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f23,plain,
( a != add(multiply(a,a),multiply(a,b))
| spl0_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f19,f14,f21]) ).
fof(f30,plain,
( a != add(multiply(a,b),multiply(a,a))
| spl0_2 ),
inference(superposition,[],[f23,f1]) ).
fof(f32,definition,
( spl0_3
<=> a = add(multiply(a,b),multiply(a,a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f34,plain,
( a != add(multiply(a,b),multiply(a,a))
| spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f30,f21,f32]) ).
fof(f41,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[],[f6,f2]) ).
fof(f77,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),multiply(X0,inverse(X1))),
inference(superposition,[],[f4,f8]) ).
fof(f91,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(forward_demodulation,[],[f77,f6]) ).
fof(f97,plain,
! [X0,X1] : add(multiply(multiplicative_identity,X0),multiply(multiplicative_identity,X1)) = add(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f18,f8]) ).
fof(f119,plain,
! [X0,X1] : add(multiply(multiplicative_identity,X0),X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f97,f41]) ).
fof(f130,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f119,f41]) ).
fof(f141,plain,
! [X0] : add(multiply(X0,X0),additive_identity) = X0,
inference(superposition,[],[f91,f10]) ).
fof(f147,plain,
! [X0] : multiply(X0,X0) = X0,
inference(forward_demodulation,[],[f141,f5]) ).
fof(f155,plain,
( a != add(multiply(a,b),a)
| spl0_3 ),
inference(backward_demodulation,[],[f34,f147]) ).
fof(f163,definition,
( spl0_9
<=> a = add(multiply(a,b),a) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f165,plain,
( a != add(multiply(a,b),a)
| spl0_9 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,plain,
( ~ spl0_9
| spl0_3 ),
inference(avatar_split_clause,[],[f155,f32,f163]) ).
fof(f241,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[],[f130,f6]) ).
fof(f255,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[],[f241,f8]) ).
fof(f271,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),multiply(X0,multiplicative_identity)),
inference(superposition,[],[f4,f255]) ).
fof(f275,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f271,f6]) ).
fof(f278,plain,
( $false
| spl0_9 ),
inference(backward_subsumption_resolution,[],[f165,f275]) ).
fof(f279,plain,
spl0_9,
inference(avatar_contradiction_clause,[],[f278]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s14,plain,
( spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f166]) ).
cnf(s17,plain,
spl0_9,
inference(sat_conversion,[],[f279]) ).
cnf(s18,plain,
spl0_3,
inference(rat,[],[s14,s17]) ).
cnf(s19,plain,
spl0_2,
inference(rat,[],[s3,s18]) ).
cnf(s20,plain,
spl0_1,
inference(rat,[],[s2,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s20]) ).
fof(f281,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n017.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 20:59:07 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 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
% 3.58/1.26 % (4025107)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.58/1.26 % (4025113)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=2427227511:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.58/1.26 % (4025115)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2749682724:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.58/1.26 % (4025116)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=997322472:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.58/1.26 % (4025117)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=254546742:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.58/1.26 % (4025114)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=125050217:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.58/1.26 % (4025112)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=1408013477:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.58/1.26 % (4025117)First to succeed.
% 3.58/1.26 % (4025115)Also succeeded, but the first one will report.
% 3.58/1.26 % (4025117)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4025107"
% 3.58/1.26 % (4025118)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2998978785:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.58/1.26 % (4025118)Also succeeded, but the first one will report.
% 3.58/1.26 % (4025116)Instruction limit reached!
% 3.58/1.26 % (4025116)------------------------------
% 3.58/1.26 % (4025116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.26 % (4025116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.26 % (4025116)CaDiCaL version: 2.1.3
% 3.58/1.26 % (4025116)Termination reason: Instruction limit
% 3.58/1.26 % (4025116)Termination phase: Saturation
% 3.58/1.26 % (4025116)Time elapsed: 0.107 s
% 3.58/1.26 % (4025116)Peak memory usage: 89 MB
% 3.58/1.26 % (4025116)Instructions burned: 183 (million)
% 3.58/1.26 % (4025126)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2899848955:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.58/1.26 % (4025117)Refutation found. Thanks to Tanya!
% 3.58/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.58/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.26 % (4025117)------------------------------
% 3.58/1.26 % (4025117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.26 % (4025117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.26 % (4025117)CaDiCaL version: 2.1.3
% 3.58/1.26 % (4025117)Termination reason: Refutation
% 3.58/1.26 % (4025117)Time elapsed: 0.011 s
% 3.58/1.26 % (4025117)Peak memory usage: 89 MB
% 3.58/1.26 % (4025117)Instructions burned: 13 (million)
% 3.58/1.26 % (4025117)------------------------------
% 3.58/1.26 % (4025117)------------------------------
% 3.58/1.26 % (4025107)Success in time 0.419 s
% 3.58/1.26 % Vampire exiting
%------------------------------------------------------------------------------