%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE141+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 : n012.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 11:40:26 AM UTC 2026
% Result : Theorem 0.06s 0.90s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 22 unt; 2 def)
% Number of atoms : 80 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 23 |; 3 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 53 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_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',distributivity1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X0] :
( leq(multiplication(strong_iteration(one),X0),strong_iteration(one))
& leq(strong_iteration(one),multiplication(strong_iteration(one),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(multiplication(strong_iteration(one),X0),strong_iteration(one))
& leq(strong_iteration(one),multiplication(strong_iteration(one),X0)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f24,plain,
? [X0] :
( ~ leq(multiplication(strong_iteration(one),X0),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
( ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f42,plain,
! [X2,X0,X1] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,definition,
( spl1_1
<=> leq(strong_iteration(one),multiplication(strong_iteration(one),sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f50,plain,
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0))
| spl1_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl1_2
<=> leq(multiplication(strong_iteration(one),sK0),strong_iteration(one)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f54,plain,
( ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one))
| spl1_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f125,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f34,f32]) ).
fof(f207,plain,
( ~ leq(strong_iteration(one),addition(multiplication(one,strong_iteration(one)),sK0))
| spl1_1 ),
inference(resolution,[],[f42,f50]) ).
fof(f210,plain,
! [X0,X1] :
( leq(X1,strong_iteration(X0))
| ~ leq(X1,addition(multiplication(X0,X1),one)) ),
inference(superposition,[],[f42,f32]) ).
fof(f211,plain,
! [X0,X1] :
( leq(X1,strong_iteration(X0))
| ~ leq(X1,addition(one,multiplication(X0,X1))) ),
inference(forward_demodulation,[],[f210,f27]) ).
fof(f213,plain,
( ~ leq(strong_iteration(one),addition(sK0,multiplication(one,strong_iteration(one))))
| spl1_1 ),
inference(forward_demodulation,[],[f207,f27]) ).
fof(f215,plain,
( ~ leq(strong_iteration(one),addition(sK0,strong_iteration(one)))
| spl1_1 ),
inference(forward_demodulation,[],[f213,f33]) ).
fof(f233,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f28,f30]) ).
fof(f453,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f45,f233]) ).
fof(f455,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f453]) ).
fof(f475,plain,
! [X0,X1] : leq(X1,addition(X0,X1)),
inference(superposition,[],[f455,f27]) ).
fof(f635,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f475,f215]) ).
fof(f659,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f635]) ).
fof(f662,plain,
( ~ leq(multiplication(strong_iteration(one),sK0),addition(one,multiplication(one,multiplication(strong_iteration(one),sK0))))
| spl1_2 ),
inference(resolution,[],[f54,f211]) ).
fof(f665,plain,
( ~ leq(multiplication(strong_iteration(one),sK0),multiplication(one,addition(one,multiplication(strong_iteration(one),sK0))))
| spl1_2 ),
inference(forward_demodulation,[],[f662,f125]) ).
fof(f666,plain,
( ~ leq(multiplication(strong_iteration(one),sK0),addition(one,multiplication(strong_iteration(one),sK0)))
| spl1_2 ),
inference(forward_demodulation,[],[f665,f33]) ).
fof(f667,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f666,f475]) ).
fof(f668,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f667]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s11,plain,
spl1_1,
inference(sat_conversion,[],[f659]) ).
cnf(s12,plain,
spl1_2,
inference(sat_conversion,[],[f668]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s12,s11]) ).
fof(f669,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 13:11:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.33 Running first-order theorem proving
% 0.06/0.33 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
% 0.06/0.90 % (2378896)Detected formulas, will run a generic FOF schedule.
% 0.06/0.90 % (2378906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3072418949:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.06/0.90 % (2378905)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=933183727:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.06/0.90 % (2378903)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=1451257870:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.06/0.90 % (2378902)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=2594151709:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.06/0.90 % (2378904)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1616666132:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.06/0.90 % (2378901)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=1110302997:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.06/0.90 % (2378907)dis-21_1_sil=8000:lcm=predicate:random_seed=1554219725: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)
% 0.06/0.90 % (2378904)Refutation not found, incomplete strategy
% 0.06/0.90 % (2378904)------------------------------
% 0.06/0.90 % (2378904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.06/0.90 % (2378904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.90 % (2378904)CaDiCaL version: 2.1.3
% 0.06/0.90 % (2378904)Termination reason: Refutation not found, incomplete strategy
% 0.06/0.90 % (2378904)Time elapsed: 0.001 s
% 0.06/0.90 % (2378904)Peak memory usage: 88 MB
% 0.06/0.90 % (2378907)Refutation not found, incomplete strategy
% 0.06/0.90 % (2378907)------------------------------
% 0.06/0.90 % (2378907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.06/0.90 % (2378907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.90 % (2378907)CaDiCaL version: 2.1.3
% 0.06/0.90 % (2378907)Termination reason: Refutation not found, incomplete strategy
% 0.06/0.90 % (2378907)Time elapsed: 0.001 s
% 0.06/0.90 % (2378907)Peak memory usage: 88 MB
% 0.06/0.90 % (2378907)Instructions burned: 1 (million)
% 0.06/0.90 % (2378906)First to succeed.
% 0.06/0.90 % (2378906)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2378896"
% 0.06/0.90 % (2378905)Also succeeded, but the first one will report.
% 0.06/0.90 % (2378907)------------------------------
% 0.06/0.90 % (2378907)------------------------------
% 0.06/0.90 % (2378904)------------------------------
% 0.06/0.90 % (2378904)------------------------------
% 0.06/0.90 % (2378906)Refutation found. Thanks to Tanya!
% 0.06/0.90 % SZS status Theorem for theBenchmark
% 0.06/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.90 % (2378906)------------------------------
% 0.06/0.90 % (2378906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.06/0.90 % (2378906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.90 % (2378906)CaDiCaL version: 2.1.3
% 0.06/0.90 % (2378906)Termination reason: Refutation
% 0.06/0.90 % (2378906)Time elapsed: 0.009 s
% 0.06/0.90 % (2378906)Peak memory usage: 90 MB
% 0.06/0.90 % (2378906)Instructions burned: 23 (million)
% 0.06/0.90 % (2378906)------------------------------
% 0.06/0.90 % (2378906)------------------------------
% 0.06/0.90 % (2378896)Success in time 0.271 s
% 0.06/0.90 % Vampire exiting
%------------------------------------------------------------------------------