%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE007+3 : 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 : 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 11:40:00 AM UTC 2026
% Result : Theorem 4.01s 1.56s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 72 ( 40 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 18 |; 17 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 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 : 39 ( 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
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(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(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,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(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1] :
( one != addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,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(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,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(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(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(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f53]) ).
fof(f71,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f49,f61]) ).
fof(f72,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f71,f36]) ).
fof(f130,plain,
one != multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),
inference(superposition,[],[f60,f43]) ).
fof(f279,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f72,f58]) ).
fof(f280,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f72,f59]) ).
fof(f300,plain,
one != multiplication(addition(sK1,c(sK1)),one),
inference(superposition,[],[f130,f280]) ).
fof(f302,plain,
one != addition(sK1,c(sK1)),
inference(forward_demodulation,[],[f300,f41]) ).
fof(f303,plain,
$false,
inference(forward_subsumption_resolution,[],[f302,f279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE007+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:04:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.01/1.56 % (3555208)Detected formulas, will run a generic FOF schedule.
% 4.01/1.56 % (3555232)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3635336358:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.01/1.56 % (3555234)dis-21_1_sil=8000:lcm=predicate:random_seed=1921317394: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)
% 4.01/1.56 % (3555234)Refutation not found, incomplete strategy
% 4.01/1.56 % (3555234)------------------------------
% 4.01/1.56 % (3555234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.56 % (3555234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.56 % (3555234)CaDiCaL version: 2.1.3
% 4.01/1.56 % (3555234)Termination reason: Refutation not found, incomplete strategy
% 4.01/1.56 % (3555234)Time elapsed: 0.002 s
% 4.01/1.56 % (3555234)Peak memory usage: 88 MB
% 4.01/1.56 % (3555234)Instructions burned: 2 (million)
% 4.01/1.56 % (3555230)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=2166432865:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.01/1.56 % (3555232)Instruction limit reached!
% 4.01/1.56 % (3555232)------------------------------
% 4.01/1.56 % (3555232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.56 % (3555232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.56 % (3555232)CaDiCaL version: 2.1.3
% 4.01/1.56 % (3555232)Termination reason: Instruction limit
% 4.01/1.56 % (3555232)Termination phase: Saturation
% 4.01/1.56 % (3555232)Time elapsed: 0.048 s
% 4.01/1.56 % (3555232)Peak memory usage: 88 MB
% 4.01/1.56 % (3555232)Instructions burned: 121 (million)
% 4.01/1.56 % (3555228)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=3035838784:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.01/1.56 % (3555229)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=355377774:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.01/1.56 % (3555233)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=591688505:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.01/1.56 % (3555233)First to succeed.
% 4.01/1.56 % (3555233)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3555208"
% 4.01/1.56 % (3555231)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2784331962:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.01/1.56 % (3555231)Refutation not found, incomplete strategy
% 4.01/1.56 % (3555231)------------------------------
% 4.01/1.56 % (3555231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.56 % (3555231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.56 % (3555231)CaDiCaL version: 2.1.3
% 4.01/1.56 % (3555231)Termination reason: Refutation not found, incomplete strategy
% 4.01/1.56 % (3555231)Time elapsed: 0.002 s
% 4.01/1.56 % (3555231)Peak memory usage: 88 MB
% 4.01/1.56 % (3555231)Instructions burned: 1 (million)
% 4.01/1.56 % (3555239)lrs+10_1_sil=8000:sp=occurrence:random_seed=3802076885:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.01/1.56 % (3555239)Also succeeded, but the first one will report.
% 4.01/1.56 % (3555233)Refutation found. Thanks to Tanya!
% 4.01/1.56 % SZS status Theorem for theBenchmark
% 4.01/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 4.01/1.56 % (3555233)------------------------------
% 4.01/1.56 % (3555233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.56 % (3555233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.56 % (3555233)CaDiCaL version: 2.1.3
% 4.01/1.56 % (3555233)Termination reason: Refutation
% 4.01/1.56 % (3555233)Time elapsed: 0.010 s
% 4.01/1.56 % (3555233)Peak memory usage: 89 MB
% 4.01/1.56 % (3555233)Instructions burned: 12 (million)
% 4.01/1.56 % (3555233)------------------------------
% 4.01/1.56 % (3555233)------------------------------
% 4.01/1.56 % (3555208)Success in time 0.485 s
% 4.01/1.56 % Vampire exiting
%------------------------------------------------------------------------------