%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE007+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 : n009.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 11:40:00 AM UTC 2026
% Result : Theorem 2.83s 1.28s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 17 unt; 2 def)
% Number of atoms : 138 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 128 ( 52 ~; 47 |; 19 &)
% ( 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 : 49 ( 0 sgn 45 !; 4 ?)
% 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)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
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(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
| ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
? [X0,X1] :
( ( ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
| ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(flattening,[],[f23]) ).
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(nnf_transformation,[],[f14]) ).
fof(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f31,plain,
( ( ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))))
| ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one) )
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f24]) ).
fof(f32,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f43,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
test(sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
test(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
( ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))))
| ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one) ),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f50]) ).
fof(f58,definition,
( spl3_1
<=> leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f59,plain,
( leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| spl3_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl3_2
<=> leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f64,plain,
( ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))))
| spl3_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f55,f62,f58]) ).
fof(f77,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f46,f56]) ).
fof(f78,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f77,f32]) ).
fof(f137,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
| spl3_1 ),
inference(superposition,[],[f60,f39]) ).
fof(f213,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f78,f53]) ).
fof(f214,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f78,f54]) ).
fof(f230,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),one),one)
| spl3_1 ),
inference(superposition,[],[f137,f214]) ).
fof(f232,plain,
( ~ leq(addition(sK1,c(sK1)),one)
| spl3_1 ),
inference(forward_demodulation,[],[f230,f37]) ).
fof(f233,plain,
( ~ leq(one,one)
| spl3_1 ),
inference(forward_demodulation,[],[f232,f213]) ).
fof(f238,plain,
( one != addition(one,one)
| spl3_1 ),
inference(resolution,[],[f233,f43]) ).
fof(f239,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f238,f35]) ).
fof(f240,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f239]) ).
fof(f241,plain,
( leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f59,f39]) ).
fof(f242,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| spl3_2 ),
inference(forward_demodulation,[],[f64,f39]) ).
fof(f243,plain,
( leq(multiplication(addition(sK1,c(sK1)),one),one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f241,f214]) ).
fof(f244,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),one))
| spl3_2 ),
inference(forward_demodulation,[],[f242,f214]) ).
fof(f245,plain,
( leq(addition(sK1,c(sK1)),one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f243,f37]) ).
fof(f246,plain,
( ~ leq(one,addition(sK1,c(sK1)))
| spl3_2 ),
inference(forward_demodulation,[],[f244,f37]) ).
fof(f247,plain,
( leq(one,one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f245,f213]) ).
fof(f248,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f246,f213]) ).
fof(f249,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f248,f247]) ).
fof(f250,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f249]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f240]) ).
cnf(s3,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f250]) ).
cnf(s4,plain,
spl3_2,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f251,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE007+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 12:58:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.83/1.28 % (2013789)Detected formulas, will run a generic FOF schedule.
% 2.83/1.28 % (2013800)dis-21_1_sil=8000:lcm=predicate:random_seed=239253113: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)
% 2.83/1.28 % (2013800)Refutation not found, incomplete strategy
% 2.83/1.28 % (2013800)------------------------------
% 2.83/1.28 % (2013800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.28 % (2013800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.28 % (2013800)CaDiCaL version: 2.1.3
% 2.83/1.28 % (2013800)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.28 % (2013800)Time elapsed: 0.002 s
% 2.83/1.28 % (2013800)Peak memory usage: 88 MB
% 2.83/1.28 % (2013800)Instructions burned: 2 (million)
% 2.83/1.28 % (2013797)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1128620795:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.83/1.28 % (2013795)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=201522782:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.83/1.28 % (2013796)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=2903289071:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.83/1.28 % (2013794)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=2773147829:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.83/1.28 % (2013798)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3896660977:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.83/1.28 % (2013799)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1712744924:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.83/1.28 % (2013797)Refutation not found, incomplete strategy
% 2.83/1.28 % (2013797)------------------------------
% 2.83/1.28 % (2013797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.28 % (2013797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.28 % (2013797)CaDiCaL version: 2.1.3
% 2.83/1.28 % (2013797)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.28 % (2013797)Time elapsed: 0.002 s
% 2.83/1.28 % (2013797)Peak memory usage: 88 MB
% 2.83/1.28 % (2013797)Instructions burned: 1 (million)
% 2.83/1.28 % (2013799)First to succeed.
% 2.83/1.28 % (2013799)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2013789"
% 2.83/1.28 % (2013798)Also succeeded, but the first one will report.
% 2.83/1.28 % (2013800)------------------------------
% 2.83/1.28 % (2013800)------------------------------
% 2.83/1.28 % (2013797)------------------------------
% 2.83/1.28 % (2013797)------------------------------
% 2.83/1.28 % (2013799)Refutation found. Thanks to Tanya!
% 2.83/1.28 % SZS status Theorem for theBenchmark
% 2.83/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.48 % (2013799)------------------------------
% 3.66/1.48 % (2013799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (2013799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (2013799)CaDiCaL version: 2.1.3
% 3.66/1.48 % (2013799)Termination reason: Refutation
% 3.66/1.48 % (2013799)Time elapsed: 0.009 s
% 3.66/1.48 % (2013799)Peak memory usage: 89 MB
% 3.66/1.48 % (2013799)Instructions burned: 11 (million)
% 3.66/1.48 % (2013799)------------------------------
% 3.66/1.48 % (2013799)------------------------------
% 3.66/1.48 % (2013789)Success in time 0.435 s
% 3.66/1.48 % Vampire exiting
%------------------------------------------------------------------------------