%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE009+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 : n018.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 3.73s 1.49s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 28 unt; 0 def)
% Number of atoms : 85 ( 53 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 75 ( 34 ~; 18 |; 17 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 50 !; 4 ?)
% 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(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(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(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] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f27,plain,
? [X0,X1] :
( one != addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1] :
( one != addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X1)
& test(X0) ),
inference(flattening,[],[f27]) ).
fof(f32,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(f33,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,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f35,plain,
( one != addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f28]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f44,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] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
test(sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
test(sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
one != addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f53]) ).
fof(f75,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f49,f61]) ).
fof(f76,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f75,f36]) ).
fof(f96,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f37,f36]) ).
fof(f137,plain,
one != addition(addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(superposition,[],[f60,f43]) ).
fof(f143,plain,
one != addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2))),
inference(forward_demodulation,[],[f137,f36]) ).
fof(f153,plain,
one != addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(sK2,c(sK2))))),
inference(forward_demodulation,[],[f143,f36]) ).
fof(f323,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f76,f58]) ).
fof(f324,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f76,f59]) ).
fof(f699,plain,
one != addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),c(sK2)))),
inference(superposition,[],[f153,f96]) ).
fof(f741,plain,
one != addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,addition(sK2,c(sK2))))),
inference(forward_demodulation,[],[f699,f36]) ).
fof(f778,plain,
one != addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,one))),
inference(forward_demodulation,[],[f741,f324]) ).
fof(f792,plain,
one != addition(multiplication(sK1,one),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))),
inference(forward_demodulation,[],[f778,f96]) ).
fof(f798,plain,
one != addition(multiplication(sK1,one),multiplication(c(sK1),addition(sK2,c(sK2)))),
inference(forward_demodulation,[],[f792,f43]) ).
fof(f801,plain,
one != addition(multiplication(sK1,one),multiplication(c(sK1),one)),
inference(forward_demodulation,[],[f798,f324]) ).
fof(f804,plain,
one != multiplication(addition(sK1,c(sK1)),one),
inference(forward_demodulation,[],[f801,f44]) ).
fof(f807,plain,
one != addition(sK1,c(sK1)),
inference(forward_demodulation,[],[f804,f41]) ).
fof(f808,plain,
$false,
inference(forward_subsumption_resolution,[],[f807,f323]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.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 13:00:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 3.73/1.49 % (2335055)Detected formulas, will run a generic FOF schedule.
% 3.73/1.49 % (2335088)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=2565580911:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.73/1.49 % (2335090)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3870201249:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.73/1.49 % (2335092)dis-21_1_sil=8000:lcm=predicate:random_seed=3432707256: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)
% 3.73/1.49 % (2335086)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=2765095397:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.73/1.49 % (2335089)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=257774216:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.73/1.49 % (2335087)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=1006741660:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.73/1.49 % (2335091)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3249814256:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.73/1.49 % (2335089)Refutation not found, incomplete strategy
% 3.73/1.49 % (2335089)------------------------------
% 3.73/1.49 % (2335089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.49 % (2335089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.49 % (2335089)CaDiCaL version: 2.1.3
% 3.73/1.49 % (2335089)Termination reason: Refutation not found, incomplete strategy
% 3.73/1.49 % (2335089)Time elapsed: 0.002 s
% 3.73/1.49 % (2335089)Peak memory usage: 88 MB
% 3.73/1.49 % (2335089)Instructions burned: 1 (million)
% 3.73/1.49 % (2335092)Refutation not found, incomplete strategy
% 3.73/1.49 % (2335092)------------------------------
% 3.73/1.49 % (2335092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.49 % (2335092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.49 % (2335092)CaDiCaL version: 2.1.3
% 3.73/1.49 % (2335092)Termination reason: Refutation not found, incomplete strategy
% 3.73/1.49 % (2335092)Time elapsed: 0.002 s
% 3.73/1.49 % (2335092)Peak memory usage: 88 MB
% 3.73/1.49 % (2335092)Instructions burned: 2 (million)
% 3.73/1.49 % (2335091)First to succeed.
% 3.73/1.49 % (2335091)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2335055"
% 3.73/1.49 % (2335090)Instruction limit reached!
% 3.73/1.49 % (2335090)------------------------------
% 3.73/1.49 % (2335090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.49 % (2335090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.49 % (2335090)CaDiCaL version: 2.1.3
% 3.73/1.49 % (2335090)Termination reason: Instruction limit
% 3.73/1.49 % (2335090)Termination phase: Saturation
% 3.73/1.49 % (2335090)Time elapsed: 0.067 s
% 3.73/1.49 % (2335090)Peak memory usage: 88 MB
% 3.73/1.49 % (2335090)Instructions burned: 120 (million)
% 3.73/1.49 % (2335100)lrs+10_1_sil=8000:sp=occurrence:random_seed=1967356167:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.73/1.49 % (2335092)------------------------------
% 3.73/1.49 % (2335092)------------------------------
% 3.73/1.49 % (2335089)------------------------------
% 3.73/1.49 % (2335089)------------------------------
% 3.73/1.49 % (2335100)Also succeeded, but the first one will report.
% 3.73/1.49 % (2335091)Refutation found. Thanks to Tanya!
% 3.73/1.49 % SZS status Theorem for theBenchmark
% 3.73/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.73/1.49 % (2335091)------------------------------
% 3.73/1.49 % (2335091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.49 % (2335091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.49 % (2335091)CaDiCaL version: 2.1.3
% 3.73/1.49 % (2335091)Termination reason: Refutation
% 3.73/1.49 % (2335091)Time elapsed: 0.020 s
% 3.73/1.49 % (2335091)Peak memory usage: 89 MB
% 3.73/1.49 % (2335091)Instructions burned: 29 (million)
% 3.73/1.49 % (2335091)------------------------------
% 3.73/1.49 % (2335091)------------------------------
% 3.73/1.49 % (2335055)Success in time 0.452 s
% 3.73/1.49 % Vampire exiting
%------------------------------------------------------------------------------