%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE010+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 11:40:36 AM UTC 2026
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 35 unt; 3 def)
% Number of atoms : 122 ( 54 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 53 ~; 33 |; 8 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1] :
( one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1] :
( one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X1)
& test(X0) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f30,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f41,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
test(sK1),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
test(sK2),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
one != addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f41]) ).
fof(f47,plain,
! [X0] :
( ~ complement(sK0(X0),X0)
| ~ test(X0) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f52,plain,
! [X0,X1] :
( complement(X1,X0)
| addition(X0,X1) = one ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f53,plain,
! [X0] :
( ~ complement(X0,c(X0))
| ~ test(X0) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f81,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK0(X0)) ),
inference(resolution,[],[f52,f47]) ).
fof(f82,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f52,f53]) ).
fof(f83,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f82,f23]) ).
fof(f88,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f24,f26]) ).
fof(f102,plain,
one != addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))),
inference(superposition,[],[f45,f24]) ).
fof(f105,plain,
one != addition(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))),
inference(forward_demodulation,[],[f102,f23]) ).
fof(f127,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f30,f28]) ).
fof(f206,plain,
one != addition(addition(multiplication(sK1,sK2),addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))),multiplication(c(sK1),addition(sK2,c(sK2)))),
inference(forward_demodulation,[],[f105,f30]) ).
fof(f207,plain,
one != addition(addition(multiplication(sK1,sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK1),addition(sK2,c(sK2)))),
inference(forward_demodulation,[],[f206,f31]) ).
fof(f245,plain,
one = addition(sK2,sK0(sK2)),
inference(resolution,[],[f81,f44]) ).
fof(f248,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f83,f43]) ).
fof(f249,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f83,f44]) ).
fof(f440,definition,
( spl3_7
<=> one = addition(sK2,sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f441,plain,
( one = addition(sK2,sK0(sK2))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f657,definition,
( spl3_13
<=> one = addition(sK1,c(sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f658,plain,
( one = addition(sK1,c(sK1))
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f1007,definition,
( spl3_16
<=> one = addition(sK2,c(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_16])],[avatar_definition]) ).
fof(f1008,plain,
( one = addition(sK2,c(sK2))
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f1663,plain,
spl3_7,
inference(avatar_split_clause,[],[f245,f440]) ).
fof(f1664,plain,
spl3_13,
inference(avatar_split_clause,[],[f248,f657]) ).
fof(f1665,plain,
spl3_16,
inference(avatar_split_clause,[],[f249,f1007]) ).
fof(f1808,plain,
( one = addition(sK2,one)
| ~ spl3_7 ),
inference(superposition,[],[f88,f441]) ).
fof(f2106,plain,
( one != addition(addition(multiplication(sK1,sK2),multiplication(one,sK1)),multiplication(c(sK1),one))
| ~ spl3_16 ),
inference(superposition,[],[f207,f1008]) ).
fof(f2130,plain,
( one != addition(addition(multiplication(sK1,sK2),multiplication(one,sK1)),c(sK1))
| ~ spl3_16 ),
inference(forward_demodulation,[],[f2106,f28]) ).
fof(f2140,plain,
( one != addition(addition(multiplication(sK1,sK2),sK1),c(sK1))
| ~ spl3_16 ),
inference(forward_demodulation,[],[f2130,f29]) ).
fof(f2149,plain,
( one != addition(addition(sK1,multiplication(sK1,sK2)),c(sK1))
| ~ spl3_16 ),
inference(forward_demodulation,[],[f2140,f23]) ).
fof(f2157,plain,
( one != addition(multiplication(sK1,addition(one,sK2)),c(sK1))
| ~ spl3_16 ),
inference(forward_demodulation,[],[f2149,f127]) ).
fof(f2162,plain,
( one != addition(multiplication(sK1,addition(sK2,one)),c(sK1))
| ~ spl3_16 ),
inference(forward_demodulation,[],[f2157,f23]) ).
fof(f2165,plain,
( one != addition(multiplication(sK1,one),c(sK1))
| ~ spl3_7
| ~ spl3_16 ),
inference(forward_demodulation,[],[f2162,f1808]) ).
fof(f2168,plain,
( one != addition(sK1,c(sK1))
| ~ spl3_7
| ~ spl3_16 ),
inference(forward_demodulation,[],[f2165,f28]) ).
fof(f2170,plain,
( $false
| ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(forward_subsumption_resolution,[],[f2168,f658]) ).
fof(f2171,plain,
( ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_contradiction_clause,[],[f2170]) ).
cnf(s30,plain,
spl3_7,
inference(sat_conversion,[],[f1663]) ).
cnf(s31,plain,
spl3_13,
inference(sat_conversion,[],[f1664]) ).
cnf(s32,plain,
spl3_16,
inference(sat_conversion,[],[f1665]) ).
cnf(s48,plain,
( ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(sat_conversion,[],[f2171]) ).
cnf(s49,plain,
~ spl3_7,
inference(rat,[],[s48,s32,s31]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s30,s49]) ).
fof(f2172,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 12:59:56 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50 % (514220)Will run a generic schedule for satisfiability detection.
% 0.21/0.50 % (514229)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1391123002:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.50 % (514228)% WARNING: option uhcvi not known.
% 0.21/0.50 % (514227)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3117684180_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.50 % (514230)dis+10_1_sil=32000:sp=arity:random_seed=197272955:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.50 % (514228)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4207352312:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.50 % (514232)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=93605691:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.50 % TRYING [1]
% 0.21/0.50 % TRYING [2]
% 0.21/0.50 % TRYING [3]
% 0.21/0.50 % (514234)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3126335895:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.50 % TRYING [4]
% 0.21/0.50 % (514233)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1313020197:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.50 % TRYING [5]
% 0.21/0.50 % (514228) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-514220-514228"...
% 0.21/0.50 % (514228)...printing done.
% 0.21/0.50 % (514228)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Theorem for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (514228)------------------------------
% 0.21/0.50 % (514228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.50 % (514228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.50 % (514228)CaDiCaL version: 2.1.3
% 0.21/0.50 % (514228)Termination reason: Refutation
% 0.21/0.50 % (514228)Time elapsed: 0.052 s
% 0.21/0.50 % (514228)Peak memory usage: 13 MB
% 0.21/0.50 % (514228)Instructions burned: 86 (million)
% 0.21/0.50 % (514220)Success in time 0.09 s
% 0.21/0.50 % Vampire exiting
%------------------------------------------------------------------------------