%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE021+3 : 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 : n006.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 3.72s 1.48s
% Output : Refutation 3.72s
% 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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
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(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)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
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] :
( addition(multiplication(X1,X0),multiplication(c(X1),X0)) != X0
& test(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f31,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(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(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f34,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)],[f27]) ).
fof(f35,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
test(sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
sK1 != addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f52]) ).
fof(f65,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f48,f59]) ).
fof(f66,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f65,f35]) ).
fof(f168,plain,
sK1 != multiplication(addition(sK2,c(sK2)),sK1),
inference(superposition,[],[f58,f43]) ).
fof(f240,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f66,f57]) ).
fof(f254,plain,
sK1 != multiplication(one,sK1),
inference(superposition,[],[f168,f240]) ).
fof(f256,plain,
$false,
inference(forward_subsumption_resolution,[],[f254,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE021+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 12:58:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.41 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
% 3.72/1.48 % (2960908)Detected formulas, will run a generic FOF schedule.
% 3.72/1.48 % (2960917)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=811316014:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.72/1.48 % (2960913)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=2601996929:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.72/1.48 % (2960915)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=3639430444:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.72/1.48 % (2960914)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=1435987262:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.72/1.48 % (2960917)Instruction limit reached!
% 3.72/1.48 % (2960917)------------------------------
% 3.72/1.48 % (2960917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.48 % (2960917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.48 % (2960917)CaDiCaL version: 2.1.3
% 3.72/1.48 % (2960917)Termination reason: Instruction limit
% 3.72/1.48 % (2960917)Termination phase: Saturation
% 3.72/1.48 % (2960917)Time elapsed: 0.038 s
% 3.72/1.48 % (2960917)Peak memory usage: 89 MB
% 3.72/1.48 % (2960917)Instructions burned: 131 (million)
% 3.72/1.48 % (2960916)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3567501025:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.72/1.48 % (2960919)dis-21_1_sil=8000:lcm=predicate:random_seed=3954825660: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)
% 3.72/1.48 % (2960916)Refutation not found, incomplete strategy
% 3.72/1.48 % (2960916)------------------------------
% 3.72/1.48 % (2960916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.48 % (2960916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.48 % (2960916)CaDiCaL version: 2.1.3
% 3.72/1.48 % (2960916)Termination reason: Refutation not found, incomplete strategy
% 3.72/1.48 % (2960916)Time elapsed: 0.002 s
% 3.72/1.48 % (2960916)Peak memory usage: 88 MB
% 3.72/1.48 % (2960919)Refutation not found, incomplete strategy
% 3.72/1.48 % (2960919)------------------------------
% 3.72/1.48 % (2960919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.48 % (2960919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.48 % (2960919)CaDiCaL version: 2.1.3
% 3.72/1.48 % (2960919)Termination reason: Refutation not found, incomplete strategy
% 3.72/1.48 % (2960919)Time elapsed: 0.002 s
% 3.72/1.48 % (2960919)Peak memory usage: 88 MB
% 3.72/1.48 % (2960919)Instructions burned: 2 (million)
% 3.72/1.48 % (2960918)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1765360045:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.72/1.48 % (2960918)First to succeed.
% 3.72/1.48 % (2960918)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2960908"
% 3.72/1.48 % (2960924)lrs+10_1_sil=8000:sp=occurrence:random_seed=1483604584:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.72/1.48 % (2960924)Also succeeded, but the first one will report.
% 3.72/1.48 % (2960919)------------------------------
% 3.72/1.48 % (2960919)------------------------------
% 3.72/1.48 % (2960916)------------------------------
% 3.72/1.48 % (2960916)------------------------------
% 3.72/1.48 % (2960918)Refutation found. Thanks to Tanya!
% 3.72/1.48 % SZS status Theorem for theBenchmark
% 3.72/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.48 % (2960918)------------------------------
% 3.72/1.48 % (2960918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.48 % (2960918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.48 % (2960918)CaDiCaL version: 2.1.3
% 3.72/1.48 % (2960918)Termination reason: Refutation
% 3.72/1.48 % (2960918)Time elapsed: 0.009 s
% 3.72/1.48 % (2960918)Peak memory usage: 89 MB
% 3.72/1.48 % (2960918)Instructions burned: 10 (million)
% 3.72/1.48 % (2960918)------------------------------
% 3.72/1.48 % (2960918)------------------------------
% 3.72/1.48 % (2960908)Success in time 0.448 s
% 3.72/1.48 % Vampire exiting
%------------------------------------------------------------------------------