%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE021+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 : n026.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 11:40:04 AM UTC 2026
% Result : Theorem 5.46s 2.07s
% Output : Refutation 5.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 62 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 59 ( 24 ~; 18 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 37 ( 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/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)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
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] :
( addition(multiplication(X1,X0),multiplication(c(X1),X0)) != X0
& test(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f25,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(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(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f19]) ).
fof(f28,plain,
( sK1 != addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))
& test(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f21]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f37,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] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
test(sK2),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
sK1 != addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f46]) ).
fof(f57,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f42,f51]) ).
fof(f58,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f57,f29]) ).
fof(f160,plain,
sK1 != multiplication(addition(sK2,c(sK2)),sK1),
inference(superposition,[],[f50,f37]) ).
fof(f182,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f58,f49]) ).
fof(f185,plain,
sK1 != multiplication(one,sK1),
inference(superposition,[],[f160,f182]) ).
fof(f187,plain,
$false,
inference(forward_subsumption_resolution,[],[f185,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE021+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n026.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Sun Sep 27 13:01:41 UTC 2026
% 0.23/0.47 % CPUTime :
% 0.23/0.47 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 5.46/2.07 % (2828202)Detected formulas, will run a generic FOF schedule.
% 5.46/2.07 % (2828207)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=256719529:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.46/2.07 % (2828210)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2170788703:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.46/2.07 % (2828210)Refutation not found, incomplete strategy
% 5.46/2.07 % (2828210)------------------------------
% 5.46/2.07 % (2828210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/2.07 % (2828210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/2.07 % (2828210)CaDiCaL version: 2.1.3
% 5.46/2.07 % (2828210)Termination reason: Refutation not found, incomplete strategy
% 5.46/2.07 % (2828210)Time elapsed: 0.003 s
% 5.46/2.07 % (2828210)Peak memory usage: 88 MB
% 5.46/2.07 % (2828213)dis-21_1_sil=8000:lcm=predicate:random_seed=772773803: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)
% 5.46/2.07 % (2828212)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=483424565:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.46/2.07 % (2828209)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=3703198062:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.46/2.07 % (2828211)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2331438735:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.46/2.07 % (2828208)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=3230843747:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.46/2.07 % (2828213)Refutation not found, incomplete strategy
% 5.46/2.07 % (2828213)------------------------------
% 5.46/2.07 % (2828213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/2.07 % (2828213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/2.07 % (2828213)CaDiCaL version: 2.1.3
% 5.46/2.07 % (2828213)Termination reason: Refutation not found, incomplete strategy
% 5.46/2.07 % (2828213)Time elapsed: 0.003 s
% 5.46/2.07 % (2828213)Peak memory usage: 88 MB
% 5.46/2.07 % (2828213)Instructions burned: 1 (million)
% 5.46/2.07 % (2828212)First to succeed.
% 5.46/2.07 % (2828212)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2828202"
% 5.46/2.07 % (2828211)Also succeeded, but the first one will report.
% 5.46/2.07 % (2828210)------------------------------
% 5.46/2.07 % (2828210)------------------------------
% 5.46/2.07 % (2828213)------------------------------
% 5.46/2.07 % (2828213)------------------------------
% 5.46/2.07 % (2828212)Refutation found. Thanks to Tanya!
% 5.46/2.07 % SZS status Theorem for theBenchmark
% 5.46/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 5.46/2.07 % (2828212)------------------------------
% 5.46/2.07 % (2828212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/2.07 % (2828212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/2.07 % (2828212)CaDiCaL version: 2.1.3
% 5.46/2.07 % (2828212)Termination reason: Refutation
% 5.46/2.07 % (2828212)Time elapsed: 0.010 s
% 5.46/2.07 % (2828212)Peak memory usage: 89 MB
% 5.46/2.07 % (2828212)Instructions burned: 7 (million)
% 5.46/2.07 % (2828212)------------------------------
% 5.46/2.07 % (2828212)------------------------------
% 5.46/2.07 % (2828202)Success in time 0.63 s
% 5.46/2.07 % Vampire exiting
%------------------------------------------------------------------------------