%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE021+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 11:40:39 AM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 16 unt; 2 def)
% Number of atoms : 101 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 35 ~; 32 |; 5 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 43 ( 0 sgn 41 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',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/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f19,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
& leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
& leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f29,plain,
? [X0,X1] :
( ( ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
| ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) )
& test(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f49,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f53,plain,
( ~ leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1)
| ~ leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
test(sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f49]) ).
fof(f57,definition,
( spl3_1
<=> leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f58,plain,
( leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( ~ leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)))
| spl3_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl3_2
<=> leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f63,plain,
( ~ leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f53,f61,f57]) ).
fof(f65,plain,
( ~ leq(sK1,multiplication(addition(sK2,c(sK2)),sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f59,f38]) ).
fof(f76,plain,
( multiplication(addition(sK2,c(sK2)),sK1) != addition(sK1,multiplication(addition(sK2,c(sK2)),sK1))
| spl3_1 ),
inference(resolution,[],[f41,f65]) ).
fof(f78,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f44,f55]) ).
fof(f79,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f78,f30]) ).
fof(f181,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f38,f36]) ).
fof(f316,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f79,f54]) ).
fof(f319,plain,
( multiplication(one,sK1) != addition(sK1,multiplication(one,sK1))
| spl3_1 ),
inference(superposition,[],[f76,f316]) ).
fof(f323,plain,
( multiplication(one,sK1) != multiplication(addition(one,one),sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f319,f181]) ).
fof(f324,plain,
( multiplication(one,sK1) != multiplication(one,sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f323,f33]) ).
fof(f325,plain,
( $false
| spl3_1 ),
inference(trivial_inequality_removal,[],[f324]) ).
fof(f326,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f327,plain,
( leq(sK1,multiplication(addition(sK2,c(sK2)),sK1))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f58,f38]) ).
fof(f328,plain,
( ~ leq(multiplication(addition(sK2,c(sK2)),sK1),sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f63,f38]) ).
fof(f329,plain,
( leq(sK1,multiplication(one,sK1))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f327,f316]) ).
fof(f330,plain,
( ~ leq(multiplication(one,sK1),sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f328,f316]) ).
fof(f331,plain,
( leq(sK1,sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f329,f36]) ).
fof(f332,plain,
( ~ leq(sK1,sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f330,f36]) ).
fof(f333,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f332,f331]) ).
fof(f334,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f333]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
spl3_1,
inference(sat_conversion,[],[f326]) ).
cnf(s5,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f334]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s5,s4]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s4]) ).
fof(f335,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE021+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 13:03:02 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.40 Running first-order model finding
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.46 % (3972561)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (3972568)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=755917984:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.46 % (3972567)% WARNING: option uhcvi not known.
% 0.13/0.46 % (3972569)dis+10_1_sil=32000:sp=arity:random_seed=1264202156:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.46 % (3972566)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1828015667_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.46 % (3972567)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2219125741:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.46 % (3972571)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2314780935:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.46 % (3972570)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=851527130:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.46 % (3972572)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2201925993:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % TRYING [1]
% 0.13/0.46 % TRYING [2]
% 0.13/0.46 % TRYING [3]
% 0.13/0.46 % (3972570) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3972561-3972570"...
% 0.13/0.46 % TRYING [4]
% 0.13/0.46 % (3972570)...printing done.
% 0.13/0.46 % (3972570)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (3972570)------------------------------
% 0.13/0.46 % (3972570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (3972570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (3972570)CaDiCaL version: 2.1.3
% 0.13/0.46 % (3972570)Termination reason: Refutation
% 0.13/0.46 % (3972570)Time elapsed: 0.010 s
% 0.13/0.46 % (3972570)Peak memory usage: 12 MB
% 0.13/0.46 % (3972570)Instructions burned: 13 (million)
% 0.13/0.46 % (3972561)Success in time 0.052 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------