%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n012.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 11:40:41 AM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 32 unt; 0 def)
% Number of atoms : 68 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 15 ~; 5 |; 10 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 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 : 59 ( 52 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
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(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
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(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(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f55,plain,
test(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f56,plain,
multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f30]) ).
fof(f69,plain,
multiplication(sK1,sK3) != addition(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(resolution,[],[f42,f57]) ).
fof(f70,plain,
multiplication(sK1,sK3) != addition(multiplication(sK1,sK3),multiplication(sK2,sK1)),
inference(forward_demodulation,[],[f69,f31]) ).
fof(f71,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK0(X0)) ),
inference(resolution,[],[f45,f44]) ).
fof(f80,plain,
one = addition(sK2,sK0(sK2)),
inference(resolution,[],[f71,f55]) ).
fof(f91,plain,
! [X0] : addition(sK2,addition(sK0(sK2),X0)) = addition(one,X0),
inference(superposition,[],[f32,f80]) ).
fof(f173,plain,
addition(sK2,sK0(sK2)) = addition(one,sK0(sK2)),
inference(superposition,[],[f91,f34]) ).
fof(f175,plain,
! [X0] : addition(one,X0) = addition(sK2,addition(X0,sK0(sK2))),
inference(superposition,[],[f91,f31]) ).
fof(f178,plain,
one = addition(one,sK0(sK2)),
inference(forward_demodulation,[],[f173,f80]) ).
fof(f186,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f39,f37]) ).
fof(f191,plain,
! [X0] : multiplication(addition(X0,multiplication(sK2,sK1)),sK3) = addition(multiplication(X0,sK3),multiplication(sK2,sK1)),
inference(superposition,[],[f39,f56]) ).
fof(f253,plain,
addition(one,one) = addition(sK2,one),
inference(superposition,[],[f175,f178]) ).
fof(f257,plain,
addition(one,one) = addition(one,sK2),
inference(forward_demodulation,[],[f253,f31]) ).
fof(f261,plain,
one = addition(one,sK2),
inference(forward_demodulation,[],[f257,f34]) ).
fof(f593,plain,
multiplication(sK1,sK3) != multiplication(addition(sK1,multiplication(sK2,sK1)),sK3),
inference(superposition,[],[f70,f191]) ).
fof(f599,plain,
multiplication(sK1,sK3) != multiplication(multiplication(addition(one,sK2),sK1),sK3),
inference(forward_demodulation,[],[f593,f186]) ).
fof(f605,plain,
multiplication(sK1,sK3) != multiplication(addition(one,sK2),multiplication(sK1,sK3)),
inference(forward_demodulation,[],[f599,f35]) ).
fof(f609,plain,
multiplication(sK1,sK3) != multiplication(one,multiplication(sK1,sK3)),
inference(forward_demodulation,[],[f605,f261]) ).
fof(f612,plain,
$false,
inference(forward_subsumption_resolution,[],[f609,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 13:03:19 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.33 Running first-order model finding
% 0.08/0.33 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
% 0.08/0.38 % (2373215)Will run a generic schedule for satisfiability detection.
% 0.08/0.38 % (2373221)% WARNING: option uhcvi not known.
% 0.08/0.38 % (2373221)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=949097443:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.38 % (2373224)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4195454364:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.38 % (2373222)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=572379383:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.38 % (2373223)dis+10_1_sil=32000:sp=arity:random_seed=2915571875:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.38 % (2373220)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2859876171_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.38 % (2373225)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3656048436:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.38 % (2373226)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=822613450:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.38 % TRYING [1]
% 0.08/0.38 % TRYING [2]
% 0.08/0.38 % TRYING [3]
% 0.08/0.38 % TRYING [4]
% 0.08/0.38 % (2373224) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2373215-2373224"...
% 0.08/0.38 % (2373224)...printing done.
% 0.08/0.38 % (2373224)Refutation found. Thanks to Tanya!
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.38 % (2373224)------------------------------
% 0.08/0.38 % (2373224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.38 % (2373224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.38 % (2373224)CaDiCaL version: 2.1.3
% 0.08/0.38 % (2373224)Termination reason: Refutation
% 0.08/0.38 % (2373224)Time elapsed: 0.009 s
% 0.08/0.38 % (2373224)Peak memory usage: 12 MB
% 0.08/0.38 % (2373224)Instructions burned: 24 (million)
% 0.08/0.38 % (2373215)Success in time 0.044 s
% 0.08/0.38 % Vampire exiting
%------------------------------------------------------------------------------