%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE022+2 : TPTP v9.3.1. Released v4.0.0.
% 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 11:40:05 AM UTC 2026
% Result : Theorem 0.18s 1.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 15 unt; 2 def)
% Number of atoms : 124 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 115 ( 48 ~; 44 |; 13 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 45 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f17,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
? [X0,X1] :
( ( ~ leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
| ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) )
& test(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f30,plain,
( ( ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1) )
& test(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f23]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
test(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
( ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f49]) ).
fof(f56,definition,
( spl3_1
<=> leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f57,plain,
( leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl3_2
<=> leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f62,plain,
( ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| spl3_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f53,f60,f56]) ).
fof(f68,plain,
( sK1 != addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| spl3_1 ),
inference(resolution,[],[f42,f58]) ).
fof(f69,plain,
( sK1 != addition(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| spl3_1 ),
inference(forward_demodulation,[],[f68,f31]) ).
fof(f71,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f45,f54]) ).
fof(f72,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f71,f31]) ).
fof(f132,plain,
( sK1 != addition(sK1,multiplication(sK1,addition(sK2,c(sK2))))
| spl3_1 ),
inference(superposition,[],[f69,f38]) ).
fof(f189,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f72,f52]) ).
fof(f192,plain,
( sK1 != addition(sK1,multiplication(sK1,one))
| spl3_1 ),
inference(superposition,[],[f132,f189]) ).
fof(f196,plain,
( sK1 != addition(sK1,sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f192,f36]) ).
fof(f197,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f196,f34]) ).
fof(f198,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f197]) ).
fof(f199,plain,
( leq(multiplication(sK1,addition(sK2,c(sK2))),sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f57,f38]) ).
fof(f200,plain,
( ~ leq(sK1,multiplication(sK1,addition(sK2,c(sK2))))
| spl3_2 ),
inference(forward_demodulation,[],[f62,f38]) ).
fof(f201,plain,
( leq(multiplication(sK1,one),sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f199,f189]) ).
fof(f202,plain,
( ~ leq(sK1,multiplication(sK1,one))
| spl3_2 ),
inference(forward_demodulation,[],[f200,f189]) ).
fof(f203,plain,
( leq(sK1,sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f201,f36]) ).
fof(f204,plain,
( ~ leq(sK1,sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f202,f36]) ).
fof(f205,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f204,f203]) ).
fof(f206,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f205]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f198]) ).
cnf(s3,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f206]) ).
cnf(s4,plain,
spl3_2,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f207,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE022+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 12:57:35 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.18/1.50 % (2532186)Detected formulas, will run a generic FOF schedule.
% 0.18/1.50 % (2532197)dis-21_1_sil=8000:lcm=predicate:random_seed=984355693:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.18/1.50 % (2532197)Refutation not found, incomplete strategy
% 0.18/1.50 % (2532197)------------------------------
% 0.18/1.50 % (2532197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (2532197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (2532197)CaDiCaL version: 2.1.3
% 0.18/1.50 % (2532197)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.50 % (2532197)Time elapsed: 0.002 s
% 0.18/1.50 % (2532197)Peak memory usage: 88 MB
% 0.18/1.50 % (2532197)Instructions burned: 2 (million)
% 0.18/1.50 % (2532194)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3738550170:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.50 % (2532191)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3233993215:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.50 % (2532195)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3317330388:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.50 % (2532193)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2213393092:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.50 % (2532192)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=727188625:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.50 % (2532196)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2140082623:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.50 % (2532194)Refutation not found, incomplete strategy
% 0.18/1.50 % (2532194)------------------------------
% 0.18/1.50 % (2532194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (2532194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (2532194)CaDiCaL version: 2.1.3
% 0.18/1.50 % (2532194)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.50 % (2532194)Time elapsed: 0.002 s
% 0.18/1.50 % (2532194)Peak memory usage: 88 MB
% 0.18/1.50 % (2532196)First to succeed.
% 0.18/1.50 % (2532196)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2532186"
% 0.18/1.50 % (2532195)Also succeeded, but the first one will report.
% 0.18/1.50 % (2532197)------------------------------
% 0.18/1.50 % (2532197)------------------------------
% 0.18/1.50 % (2532194)------------------------------
% 0.18/1.50 % (2532194)------------------------------
% 0.18/1.50 % (2532205)lrs+10_1_sil=8000:sp=occurrence:random_seed=2852133622:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.18/1.50 % (2532205)Also succeeded, but the first one will report.
% 0.18/1.50 % (2532196)Refutation found. Thanks to Tanya!
% 0.18/1.50 % SZS status Theorem for theBenchmark
% 0.18/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.50 % (2532196)------------------------------
% 0.18/1.50 % (2532196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (2532196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (2532196)CaDiCaL version: 2.1.3
% 0.18/1.50 % (2532196)Termination reason: Refutation
% 0.18/1.50 % (2532196)Time elapsed: 0.007 s
% 0.18/1.50 % (2532196)Peak memory usage: 89 MB
% 0.18/1.50 % (2532196)Instructions burned: 8 (million)
% 0.18/1.50 % (2532196)------------------------------
% 0.18/1.50 % (2532196)------------------------------
% 0.18/1.50 % (2532186)Success in time 0.431 s
% 0.18/1.50 % Vampire exiting
%------------------------------------------------------------------------------