%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE009+1 : 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 : n014.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 2.60s 1.36s
% Output : Refutation 2.60s
% 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/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
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(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/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/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(f17,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,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,[],[f18]) ).
fof(f22,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,[],[f21]) ).
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(f28,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f19]) ).
fof(f29,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)],[f22]) ).
fof(f30,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
test(sK1),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
test(sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
one != addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f47]) ).
fof(f67,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f43,f53]) ).
fof(f68,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f67,f30]) ).
fof(f88,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f31,f30]) ).
fof(f129,plain,
one != addition(addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(superposition,[],[f52,f37]) ).
fof(f135,plain,
one != addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2))),
inference(forward_demodulation,[],[f129,f30]) ).
fof(f145,plain,
one != addition(multiplication(c(sK1),c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(sK1,addition(sK2,c(sK2))))),
inference(forward_demodulation,[],[f135,f30]) ).
fof(f190,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f68,f50]) ).
fof(f191,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f68,f51]) ).
fof(f460,plain,
one != addition(multiplication(c(sK1),sK2),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),c(sK2)))),
inference(superposition,[],[f145,f88]) ).
fof(f502,plain,
one != addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,addition(sK2,c(sK2))))),
inference(forward_demodulation,[],[f460,f30]) ).
fof(f539,plain,
one != addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,one))),
inference(forward_demodulation,[],[f502,f191]) ).
fof(f553,plain,
one != addition(multiplication(sK1,one),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))),
inference(forward_demodulation,[],[f539,f88]) ).
fof(f559,plain,
one != addition(multiplication(sK1,one),multiplication(c(sK1),addition(sK2,c(sK2)))),
inference(forward_demodulation,[],[f553,f37]) ).
fof(f562,plain,
one != addition(multiplication(sK1,one),multiplication(c(sK1),one)),
inference(forward_demodulation,[],[f559,f191]) ).
fof(f565,plain,
one != multiplication(addition(sK1,c(sK1)),one),
inference(forward_demodulation,[],[f562,f38]) ).
fof(f568,plain,
one != addition(sK1,c(sK1)),
inference(forward_demodulation,[],[f565,f35]) ).
fof(f569,plain,
$false,
inference(forward_subsumption_resolution,[],[f568,f190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n014.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 12:58:17 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.60/1.36 % (797499)Detected formulas, will run a generic FOF schedule.
% 2.60/1.36 % (797556)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3283721774:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.36 % (797556)First to succeed.
% 2.60/1.36 % (797556)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-797499"
% 2.60/1.36 % (797553)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=2350158053:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.36 % (797554)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3160403957:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.36 % (797557)dis-21_1_sil=8000:lcm=predicate:random_seed=3256256669: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)
% 2.60/1.36 % (797551)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=2236339706:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.36 % (797552)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=1219848840:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.36 % (797555)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=990690063:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.36 % (797554)Refutation not found, incomplete strategy
% 2.60/1.36 % (797554)------------------------------
% 2.60/1.36 % (797554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.36 % (797554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.36 % (797554)CaDiCaL version: 2.1.3
% 2.60/1.36 % (797554)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.36 % (797554)Time elapsed: 0.002 s
% 2.60/1.36 % (797554)Peak memory usage: 88 MB
% 2.60/1.36 % (797554)Instructions burned: 1 (million)
% 2.60/1.36 % (797557)Refutation not found, incomplete strategy
% 2.60/1.36 % (797557)------------------------------
% 2.60/1.36 % (797557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.36 % (797557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.36 % (797557)CaDiCaL version: 2.1.3
% 2.60/1.36 % (797557)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.36 % (797557)Time elapsed: 0.002 s
% 2.60/1.36 % (797557)Peak memory usage: 88 MB
% 2.60/1.36 % (797557)Instructions burned: 2 (million)
% 2.60/1.36 % (797555)Instruction limit reached!
% 2.60/1.36 % (797555)------------------------------
% 2.60/1.36 % (797555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.36 % (797555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.36 % (797555)CaDiCaL version: 2.1.3
% 2.60/1.36 % (797555)Termination reason: Instruction limit
% 2.60/1.36 % (797555)Termination phase: Saturation
% 2.60/1.36 % (797555)Time elapsed: 0.069 s
% 2.60/1.36 % (797555)Peak memory usage: 89 MB
% 2.60/1.36 % (797555)Instructions burned: 121 (million)
% 2.60/1.36 % (797556)Refutation found. Thanks to Tanya!
% 2.60/1.36 % SZS status Theorem for theBenchmark
% 2.60/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.36 % (797556)------------------------------
% 2.60/1.36 % (797556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.36 % (797556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.36 % (797556)CaDiCaL version: 2.1.3
% 2.60/1.36 % (797556)Termination reason: Refutation
% 2.60/1.36 % (797556)Time elapsed: 0.008 s
% 2.60/1.36 % (797556)Peak memory usage: 89 MB
% 2.60/1.36 % (797556)Instructions burned: 22 (million)
% 2.60/1.36 % (797556)------------------------------
% 2.60/1.36 % (797556)------------------------------
% 2.60/1.36 % (797499)Success in time 0.281 s
% 2.60/1.36 % Vampire exiting
%------------------------------------------------------------------------------