%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE021+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 : n017.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 11:40:05 AM UTC 2026
% Result : Theorem 3.93s 1.52s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 13 unt; 0 def)
% Number of atoms : 107 ( 36 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 58 ~; 43 |; 13 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 59 !; 2 ?)
% 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(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(f17,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
& leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
& leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
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,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
| ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) )
& test(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
( ( ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0) )
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f26,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(f27,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,[],[f26]) ).
fof(f31,plain,
test(sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
( ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),sK0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X0,X1] :
( c(X0) = X1
| ~ complement(X0,X1)
| ~ test(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f54,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f41]) ).
fof(f68,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f38,f35]) ).
fof(f74,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f68]) ).
fof(f77,plain,
! [X0,X1] :
( addition(X0,X1) = one
| ~ complement(X0,X1) ),
inference(superposition,[],[f46,f37]) ).
fof(f123,plain,
! [X0] :
( ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(X0,sK0)))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(X0,sK0)),sK0)
| ~ complement(sK1,X0)
| ~ test(sK1) ),
inference(superposition,[],[f32,f42]) ).
fof(f130,plain,
! [X0] :
( ~ leq(sK0,addition(multiplication(sK1,sK0),multiplication(X0,sK0)))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(X0,sK0)),sK0)
| ~ complement(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f123,f31]) ).
fof(f323,plain,
! [X0] :
( ~ leq(sK0,multiplication(addition(sK1,X0),sK0))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(X0,sK0)),sK0)
| ~ complement(sK1,X0) ),
inference(forward_demodulation,[],[f130,f33]) ).
fof(f324,plain,
! [X0] :
( ~ leq(sK0,multiplication(addition(sK1,X0),sK0))
| ~ leq(multiplication(addition(sK1,X0),sK0),sK0)
| ~ complement(sK1,X0) ),
inference(forward_demodulation,[],[f323,f33]) ).
fof(f516,plain,
! [X0] :
( ~ leq(sK0,multiplication(one,sK0))
| ~ leq(multiplication(one,sK0),sK0)
| ~ complement(sK1,X0)
| ~ complement(sK1,X0) ),
inference(superposition,[],[f324,f77]) ).
fof(f517,plain,
! [X0] :
( ~ leq(sK0,multiplication(one,sK0))
| ~ leq(multiplication(one,sK0),sK0)
| ~ complement(sK1,X0) ),
inference(duplicate_literal_removal,[],[f516]) ).
fof(f520,plain,
! [X0] :
( ~ leq(sK0,sK0)
| ~ leq(multiplication(one,sK0),sK0)
| ~ complement(sK1,X0) ),
inference(forward_demodulation,[],[f517,f52]) ).
fof(f522,plain,
! [X0] :
( ~ leq(multiplication(one,sK0),sK0)
| ~ complement(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f520,f74]) ).
fof(f524,plain,
! [X0] :
( ~ leq(sK0,sK0)
| ~ complement(sK1,X0) ),
inference(forward_demodulation,[],[f522,f52]) ).
fof(f526,plain,
! [X0] : ~ complement(sK1,X0),
inference(forward_subsumption_resolution,[],[f524,f74]) ).
fof(f528,plain,
~ test(sK1),
inference(resolution,[],[f526,f54]) ).
fof(f529,plain,
$false,
inference(forward_subsumption_resolution,[],[f528,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 12:54:05 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.93/1.52 % (2526832)Detected formulas, will run a generic FOF schedule.
% 3.93/1.52 % (2526930)dis-21_1_sil=8000:lcm=predicate:random_seed=2511024745: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)
% 3.93/1.52 % (2526930)Refutation not found, incomplete strategy
% 3.93/1.52 % (2526930)------------------------------
% 3.93/1.52 % (2526930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.52 % (2526930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.52 % (2526930)CaDiCaL version: 2.1.3
% 3.93/1.52 % (2526930)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.52 % (2526930)Time elapsed: 0.002 s
% 3.93/1.52 % (2526930)Peak memory usage: 88 MB
% 3.93/1.52 % (2526930)Instructions burned: 2 (million)
% 3.93/1.52 % (2526926)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=1553800488:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.93/1.52 % (2526924)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=3455994779:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.93/1.52 % (2526925)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=2106345923:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.93/1.52 % (2526927)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1393509891:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.93/1.52 % (2526928)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=368628795:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.93/1.52 % (2526927)Refutation not found, incomplete strategy
% 3.93/1.52 % (2526927)------------------------------
% 3.93/1.52 % (2526927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.52 % (2526927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.52 % (2526927)CaDiCaL version: 2.1.3
% 3.93/1.52 % (2526927)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.52 % (2526927)Time elapsed: 0.002 s
% 3.93/1.52 % (2526927)Peak memory usage: 88 MB
% 3.93/1.52 % (2526929)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3734747619:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.93/1.52 % (2526928)First to succeed.
% 3.93/1.52 % (2526928)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2526832"
% 3.93/1.52 % (2526929)Also succeeded, but the first one will report.
% 3.93/1.52 % (2526930)------------------------------
% 3.93/1.52 % (2526930)------------------------------
% 3.93/1.52 % (2526966)lrs+10_1_sil=8000:sp=occurrence:random_seed=2847007195:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.93/1.52 % (2526966)Also succeeded, but the first one will report.
% 3.93/1.52 % (2526927)------------------------------
% 3.93/1.52 % (2526927)------------------------------
% 3.93/1.52 % (2526928)Refutation found. Thanks to Tanya!
% 3.93/1.52 % SZS status Theorem for theBenchmark
% 3.93/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.52 % (2526928)------------------------------
% 3.93/1.52 % (2526928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.52 % (2526928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.52 % (2526928)CaDiCaL version: 2.1.3
% 3.93/1.52 % (2526928)Termination reason: Refutation
% 3.93/1.52 % (2526928)Time elapsed: 0.013 s
% 3.93/1.52 % (2526928)Peak memory usage: 88 MB
% 3.93/1.52 % (2526928)Instructions burned: 18 (million)
% 3.93/1.52 % (2526928)------------------------------
% 3.93/1.52 % (2526928)------------------------------
% 3.93/1.52 % (2526832)Success in time 0.462 s
% 3.93/1.52 % Vampire exiting
%------------------------------------------------------------------------------