%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE021+2 : 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 : n007.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 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 17 unt; 2 def)
% Number of atoms : 96 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 76 ( 32 ~; 29 |; 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 : 39 ( 0 sgn 37 !; 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(f17,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(f18,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)],[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(X1,X0),multiplication(c(X1),X0)))
| ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) )
& test(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f43,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
( ~ leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1)
| ~ leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
test(sK2),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f43]) ).
fof(f49,definition,
( spl3_1
<=> leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f50,plain,
( leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( ~ leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)))
| spl3_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,definition,
( spl3_2
<=> leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f55,plain,
( ~ leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f45,f53,f49]) ).
fof(f57,plain,
( ~ leq(sK1,multiplication(addition(sK2,c(sK2)),sK1))
| spl3_1 ),
inference(forward_demodulation,[],[f51,f32]) ).
fof(f61,plain,
complement(sK2,c(sK2)),
inference(resolution,[],[f47,f46]) ).
fof(f68,plain,
( multiplication(addition(sK2,c(sK2)),sK1) != addition(sK1,multiplication(addition(sK2,c(sK2)),sK1))
| spl3_1 ),
inference(resolution,[],[f35,f57]) ).
fof(f70,plain,
one = addition(c(sK2),sK2),
inference(resolution,[],[f38,f61]) ).
fof(f71,plain,
one = addition(sK2,c(sK2)),
inference(forward_demodulation,[],[f70,f24]) ).
fof(f74,plain,
( multiplication(one,sK1) != addition(sK1,multiplication(one,sK1))
| spl3_1 ),
inference(superposition,[],[f68,f71]) ).
fof(f77,plain,
( sK1 != addition(sK1,sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f74,f30]) ).
fof(f78,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f77,f27]) ).
fof(f79,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f78]) ).
fof(f80,plain,
( leq(sK1,multiplication(addition(sK2,c(sK2)),sK1))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f50,f32]) ).
fof(f81,plain,
( ~ leq(multiplication(addition(sK2,c(sK2)),sK1),sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f55,f32]) ).
fof(f82,plain,
( leq(sK1,multiplication(one,sK1))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f80,f71]) ).
fof(f83,plain,
( ~ leq(multiplication(one,sK1),sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f81,f71]) ).
fof(f84,plain,
( leq(sK1,sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f82,f30]) ).
fof(f85,plain,
( ~ leq(sK1,sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f83,f30]) ).
fof(f86,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f85,f84]) ).
fof(f87,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f86]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
spl3_2,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f88,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 12:56:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.44 % (1397240)Will run a generic schedule for satisfiability detection.
% 0.13/0.44 % (1397250)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3854323589:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.44 % (1397246)% WARNING: option uhcvi not known.
% 0.13/0.44 % (1397251)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3737190333:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.44 % (1397245)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2972501642_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.44 % (1397249)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=122467862:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.44 % (1397246)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3806727400:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.44 % (1397247)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2994720995:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.44 % (1397248)dis+10_1_sil=32000:sp=arity:random_seed=254994814:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.44 % TRYING [1]
% 0.13/0.44 % TRYING [2]
% 0.13/0.44 % (1397249) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1397240-1397249"...
% 0.13/0.44 % TRYING [3]
% 0.13/0.44 % (1397249)...printing done.
% 0.13/0.44 % (1397249)Refutation found. Thanks to Tanya!
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.44 % (1397249)------------------------------
% 0.13/0.44 % (1397249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.44 % (1397249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.44 % (1397249)CaDiCaL version: 2.1.3
% 0.13/0.44 % (1397249)Termination reason: Refutation
% 0.13/0.44 % (1397249)Time elapsed: 0.004 s
% 0.13/0.44 % (1397249)Peak memory usage: 12 MB
% 0.13/0.44 % (1397249)Instructions burned: 4 (million)
% 0.13/0.44 % (1397240)Success in time 0.037 s
% 0.13/0.44 % Vampire exiting
%------------------------------------------------------------------------------