%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE007+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:40:01 AM UTC 2026
% Result : Theorem 0.57s 1.03s
% Output : Refutation 3.37s
% 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/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f19,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,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)],[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(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,[],[f20]) ).
fof(f30,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,[],[f29]) ).
fof(f34,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(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f37,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)],[f30]) ).
fof(f38,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f45,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f49,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f52,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
test(sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f62,plain,
test(sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f63,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,[],[f37]) ).
fof(f64,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f56]) ).
fof(f66,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(f67,plain,
( leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| spl3_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f70,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(f72,plain,
( ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))))
| spl3_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f63,f70,f66]) ).
fof(f85,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f52,f64]) ).
fof(f86,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f85,f38]) ).
fof(f145,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
| spl3_1 ),
inference(superposition,[],[f68,f45]) ).
fof(f295,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f86,f61]) ).
fof(f296,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f86,f62]) ).
fof(f319,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),one),one)
| spl3_1 ),
inference(superposition,[],[f145,f296]) ).
fof(f321,plain,
( ~ leq(addition(sK1,c(sK1)),one)
| spl3_1 ),
inference(forward_demodulation,[],[f319,f43]) ).
fof(f322,plain,
( ~ leq(one,one)
| spl3_1 ),
inference(forward_demodulation,[],[f321,f295]) ).
fof(f327,plain,
( one != addition(one,one)
| spl3_1 ),
inference(resolution,[],[f322,f49]) ).
fof(f328,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f327,f41]) ).
fof(f329,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f328]) ).
fof(f330,plain,
( leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f67,f45]) ).
fof(f331,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| spl3_2 ),
inference(forward_demodulation,[],[f72,f45]) ).
fof(f332,plain,
( leq(multiplication(addition(sK1,c(sK1)),one),one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f330,f296]) ).
fof(f333,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),one))
| spl3_2 ),
inference(forward_demodulation,[],[f331,f296]) ).
fof(f334,plain,
( leq(addition(sK1,c(sK1)),one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f332,f43]) ).
fof(f335,plain,
( ~ leq(one,addition(sK1,c(sK1)))
| spl3_2 ),
inference(forward_demodulation,[],[f333,f43]) ).
fof(f336,plain,
( leq(one,one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f334,f295]) ).
fof(f337,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f335,f295]) ).
fof(f338,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f337,f336]) ).
fof(f339,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f338]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f73]) ).
cnf(s3,plain,
spl3_1,
inference(sat_conversion,[],[f329]) ).
cnf(s4,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f339]) ).
cnf(s5,plain,
spl3_2,
inference(rat,[],[s4,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
fof(f340,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE007+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 13:04:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/1.03 % (3556067)Detected formulas, will run a generic FOF schedule.
% 0.57/1.03 % (3556077)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1247610149:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.57/1.03 % (3556074)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=2571946839:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.57/1.03 % (3556076)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2396926102:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.57/1.03 % (3556078)dis-21_1_sil=8000:lcm=predicate:random_seed=3599595290: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)
% 0.57/1.03 % (3556072)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=3238620563:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.57/1.03 % (3556075)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=593387725:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.57/1.03 % (3556073)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=1549663630:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.57/1.03 % (3556075)Refutation not found, incomplete strategy
% 0.57/1.03 % (3556075)------------------------------
% 0.57/1.03 % (3556075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.57/1.03 % (3556075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/1.03 % (3556075)CaDiCaL version: 2.1.3
% 0.57/1.03 % (3556075)Termination reason: Refutation not found, incomplete strategy
% 0.57/1.03 % (3556075)Time elapsed: 0.002 s
% 0.57/1.03 % (3556075)Peak memory usage: 88 MB
% 0.57/1.03 % (3556075)Instructions burned: 2 (million)
% 0.57/1.03 % (3556078)Refutation not found, incomplete strategy
% 0.57/1.03 % (3556078)------------------------------
% 0.57/1.03 % (3556078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.57/1.03 % (3556078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/1.03 % (3556078)CaDiCaL version: 2.1.3
% 0.57/1.03 % (3556078)Termination reason: Refutation not found, incomplete strategy
% 0.57/1.03 % (3556078)Time elapsed: 0.002 s
% 0.57/1.03 % (3556078)Peak memory usage: 88 MB
% 0.57/1.03 % (3556078)Instructions burned: 2 (million)
% 0.57/1.03 % (3556077)First to succeed.
% 0.57/1.03 % (3556077)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3556067"
% 0.57/1.03 % (3556076)Instruction limit reached!
% 0.57/1.03 % (3556076)------------------------------
% 0.57/1.03 % (3556076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.57/1.03 % (3556076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/1.03 % (3556076)CaDiCaL version: 2.1.3
% 0.57/1.03 % (3556076)Termination reason: Instruction limit
% 0.57/1.03 % (3556076)Termination phase: Saturation
% 0.57/1.03 % (3556076)Time elapsed: 0.068 s
% 0.57/1.03 % (3556076)Peak memory usage: 88 MB
% 0.57/1.03 % (3556076)Instructions burned: 120 (million)
% 0.57/1.03 % (3556086)lrs+10_1_sil=8000:sp=occurrence:random_seed=3696091476:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.57/1.03 % (3556075)------------------------------
% 0.57/1.03 % (3556075)------------------------------
% 0.57/1.03 % (3556078)------------------------------
% 0.57/1.03 % (3556078)------------------------------
% 0.57/1.03 % (3556077)Refutation found. Thanks to Tanya!
% 0.57/1.03 % SZS status Theorem for theBenchmark
% 0.57/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.23 % (3556077)------------------------------
% 3.37/1.23 % (3556077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.23 % (3556077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.23 % (3556077)CaDiCaL version: 2.1.3
% 3.37/1.23 % (3556077)Termination reason: Refutation
% 3.37/1.23 % (3556077)Time elapsed: 0.011 s
% 3.37/1.23 % (3556077)Peak memory usage: 90 MB
% 3.37/1.23 % (3556077)Instructions burned: 14 (million)
% 3.37/1.23 % (3556077)------------------------------
% 3.37/1.23 % (3556077)------------------------------
% 3.37/1.23 % (3556067)Success in time 0.421 s
% 3.37/1.23 % Vampire exiting
%------------------------------------------------------------------------------