%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE026+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 : 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 11:40:06 AM UTC 2026
% Result : Theorem 2.85s 1.38s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 27 unt; 0 def)
% Number of atoms : 97 ( 56 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 77 ( 27 ~; 20 |; 20 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',left_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(f19,conjecture,
! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
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,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X1)
& test(X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X1)
& test(X2) ),
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(multiplication(sK2,sK1),multiplication(sK1,sK3))
& multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3)
& test(sK2)
& test(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f30]) ).
fof(f38,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f42,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f46,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
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(f62,plain,
test(sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f63,plain,
multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f64,plain,
~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f65,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f56]) ).
fof(f70,plain,
multiplication(sK1,sK3) != addition(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(resolution,[],[f49,f64]) ).
fof(f71,plain,
multiplication(sK1,sK3) != addition(multiplication(sK1,sK3),multiplication(sK2,sK1)),
inference(forward_demodulation,[],[f70,f38]) ).
fof(f73,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f52,f65]) ).
fof(f74,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f73,f38]) ).
fof(f87,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f39,f41]) ).
fof(f112,plain,
multiplication(sK2,sK1) = multiplication(sK2,multiplication(sK1,sK3)),
inference(superposition,[],[f42,f63]) ).
fof(f174,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f46,f44]) ).
fof(f406,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f74,f62]) ).
fof(f497,plain,
one = addition(sK2,one),
inference(superposition,[],[f87,f406]) ).
fof(f511,plain,
one = addition(one,sK2),
inference(forward_demodulation,[],[f497,f38]) ).
fof(f1174,plain,
addition(multiplication(sK1,sK3),multiplication(sK2,sK1)) = multiplication(addition(one,sK2),multiplication(sK1,sK3)),
inference(superposition,[],[f174,f112]) ).
fof(f1215,plain,
addition(multiplication(sK1,sK3),multiplication(sK2,sK1)) = multiplication(one,multiplication(sK1,sK3)),
inference(forward_demodulation,[],[f1174,f511]) ).
fof(f1233,plain,
multiplication(sK1,sK3) = addition(multiplication(sK1,sK3),multiplication(sK2,sK1)),
inference(forward_demodulation,[],[f1215,f44]) ).
fof(f1239,plain,
$false,
inference(forward_subsumption_resolution,[],[f1233,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 13:09:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.85/1.38 % (3557062)Detected formulas, will run a generic FOF schedule.
% 2.85/1.38 % (3557076)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3191927859:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.85/1.38 % (3557076)First to succeed.
% 2.85/1.38 % (3557076)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3557062"
% 2.85/1.38 % (3557073)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=673687184:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.85/1.38 % (3557072)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=3898540275:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.85/1.38 % (3557074)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2241151560:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.85/1.38 % (3557071)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=3562291637:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.85/1.38 % (3557074)Refutation not found, incomplete strategy
% 2.85/1.38 % (3557074)------------------------------
% 2.85/1.38 % (3557074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.38 % (3557074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.38 % (3557074)CaDiCaL version: 2.1.3
% 2.85/1.38 % (3557074)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.38 % (3557074)Time elapsed: 0.002 s
% 2.85/1.38 % (3557074)Peak memory usage: 88 MB
% 2.85/1.38 % (3557075)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2297477049:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.85/1.38 % (3557077)dis-21_1_sil=8000:lcm=predicate:random_seed=1435340388: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)
% 2.85/1.38 % (3557077)Refutation not found, incomplete strategy
% 2.85/1.38 % (3557077)------------------------------
% 2.85/1.38 % (3557077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.38 % (3557077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.38 % (3557077)CaDiCaL version: 2.1.3
% 2.85/1.38 % (3557077)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.38 % (3557077)Time elapsed: 0.003 s
% 2.85/1.38 % (3557077)Peak memory usage: 88 MB
% 2.85/1.38 % (3557077)Instructions burned: 2 (million)
% 2.85/1.38 % (3557075)Instruction limit reached!
% 2.85/1.38 % (3557075)------------------------------
% 2.85/1.38 % (3557075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.38 % (3557075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.38 % (3557075)CaDiCaL version: 2.1.3
% 2.85/1.38 % (3557075)Termination reason: Instruction limit
% 2.85/1.38 % (3557075)Termination phase: Saturation
% 2.85/1.38 % (3557075)Time elapsed: 0.066 s
% 2.85/1.38 % (3557075)Peak memory usage: 88 MB
% 2.85/1.38 % (3557075)Instructions burned: 119 (million)
% 2.85/1.38 % (3557076)Refutation found. Thanks to Tanya!
% 2.85/1.38 % SZS status Theorem for theBenchmark
% 2.85/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.85/1.38 % (3557076)------------------------------
% 2.85/1.38 % (3557076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.38 % (3557076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.38 % (3557076)CaDiCaL version: 2.1.3
% 2.85/1.38 % (3557076)Termination reason: Refutation
% 2.85/1.38 % (3557076)Time elapsed: 0.016 s
% 2.85/1.38 % (3557076)Peak memory usage: 89 MB
% 2.85/1.38 % (3557076)Instructions burned: 43 (million)
% 2.85/1.38 % (3557076)------------------------------
% 2.85/1.38 % (3557076)------------------------------
% 2.85/1.38 % (3557062)Success in time 0.319 s
% 2.85/1.38 % Vampire exiting
%------------------------------------------------------------------------------