%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE131+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 : n004.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 11:40:25 AM UTC 2026
% Result : Theorem 5.42s 1.80s
% Output : Refutation 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 62 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 76 !; 1 ?)
% 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
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(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_difference) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divergence1) ).
fof(f29,conjecture,
! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
? [X0] :
( zero != divergence(X0)
& ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
( zero != divergence(sK0)
& ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f32]) ).
fof(f34,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f41,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f43,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f47,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f48,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f54,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f59,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f61,plain,
! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))),
inference(cnf_transformation,[],[f33]) ).
fof(f62,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f33]) ).
fof(f63,plain,
zero = antidomain(one),
inference(superposition,[],[f45,f39]) ).
fof(f65,plain,
! [X0] : antidomain(domain(X0)) = domain(antidomain(X0)),
inference(superposition,[],[f48,f48]) ).
fof(f66,plain,
! [X0] : zero = multiplication(domain(X0),antidomain(X0)),
inference(superposition,[],[f45,f48]) ).
fof(f76,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f47,f34]) ).
fof(f77,plain,
! [X0] : one = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[],[f76,f48]) ).
fof(f78,plain,
! [X0] : one = addition(domain(X0),antidomain(X0)),
inference(forward_demodulation,[],[f77,f34]) ).
fof(f84,plain,
one = addition(domain(one),zero),
inference(superposition,[],[f78,f63]) ).
fof(f85,plain,
one = domain(one),
inference(forward_demodulation,[],[f84,f36]) ).
fof(f88,plain,
forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one))) = addition(one,forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one)))),
inference(superposition,[],[f61,f85]) ).
fof(f107,plain,
! [X0,X1] : one = addition(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))),
inference(superposition,[],[f78,f55]) ).
fof(f108,plain,
! [X0,X1] : forward_diamond(star(sK0),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0,forward_diamond(X0,X1)))) = addition(forward_diamond(X0,X1),forward_diamond(star(sK0),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0,forward_diamond(X0,X1))))),
inference(superposition,[],[f61,f55]) ).
fof(f110,plain,
! [X0] : forward_diamond(star(sK0),domain_difference(divergence(X0),forward_diamond(sK0,divergence(X0)))) = addition(divergence(X0),forward_diamond(star(sK0),domain_difference(divergence(X0),forward_diamond(sK0,divergence(X0))))),
inference(superposition,[],[f108,f59]) ).
fof(f117,plain,
! [X0] : addition(forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one))),X0) = addition(one,addition(forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one))),X0)),
inference(superposition,[],[f35,f88]) ).
fof(f135,plain,
! [X0] : addition(X0,forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one)))) = addition(one,addition(X0,forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one))))),
inference(superposition,[],[f117,f34]) ).
fof(f168,plain,
! [X0,X1] : addition(addition(X0,forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one)))),X1) = addition(one,addition(addition(X0,forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one)))),X1)),
inference(superposition,[],[f35,f135]) ).
fof(f169,plain,
! [X0,X1] : addition(X0,addition(forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one))),X1)) = addition(one,addition(X0,addition(forward_diamond(star(sK0),domain_difference(one,forward_diamond(sK0,one))),X1))),
inference(forward_demodulation,[],[f168,f35]) ).
fof(f184,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(superposition,[],[f41,f45]) ).
fof(f193,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[],[f184,f36]) ).
fof(f252,plain,
forward_diamond(star(sK0),domain_difference(divergence(sK0),divergence(sK0))) = addition(divergence(sK0),forward_diamond(star(sK0),domain_difference(divergence(sK0),divergence(sK0)))),
inference(superposition,[],[f110,f59]) ).
fof(f399,plain,
! [X0] : zero = domain_difference(X0,X0),
inference(forward_demodulation,[],[f66,f54]) ).
fof(f402,plain,
forward_diamond(star(sK0),zero) = addition(divergence(sK0),forward_diamond(star(sK0),zero)),
inference(superposition,[],[f252,f399]) ).
fof(f949,plain,
! [X0] : addition(X0,one) = addition(one,addition(X0,one)),
inference(superposition,[],[f169,f107]) ).
fof(f1968,plain,
! [X0] : multiplication(antidomain(addition(X0,one)),one) = multiplication(antidomain(addition(X0,one)),addition(X0,one)),
inference(superposition,[],[f193,f949]) ).
fof(f2035,plain,
! [X0] : zero = multiplication(antidomain(addition(X0,one)),one),
inference(forward_demodulation,[],[f1968,f45]) ).
fof(f2053,plain,
! [X0] : zero = antidomain(addition(X0,one)),
inference(forward_demodulation,[],[f2035,f39]) ).
fof(f2074,plain,
! [X0] : one = addition(domain(addition(X0,one)),zero),
inference(superposition,[],[f78,f2053]) ).
fof(f2087,plain,
! [X0] : one = domain(addition(X0,one)),
inference(forward_demodulation,[],[f2074,f36]) ).
fof(f2419,plain,
! [X0] : antidomain(one) = domain(antidomain(addition(X0,one))),
inference(superposition,[],[f65,f2087]) ).
fof(f2436,plain,
antidomain(one) = domain(zero),
inference(forward_demodulation,[],[f2419,f2053]) ).
fof(f2444,plain,
zero = domain(zero),
inference(forward_demodulation,[],[f2436,f63]) ).
fof(f2556,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(superposition,[],[f55,f2444]) ).
fof(f2581,plain,
! [X0] : domain(zero) = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f2556,f43]) ).
fof(f2586,plain,
! [X0] : zero = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f2581,f2444]) ).
fof(f2957,plain,
zero = addition(divergence(sK0),zero),
inference(superposition,[],[f402,f2586]) ).
fof(f2966,plain,
zero = divergence(sK0),
inference(forward_demodulation,[],[f2957,f36]) ).
fof(f2972,plain,
$false,
inference(forward_subsumption_resolution,[],[f2966,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE131+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 13:11:36 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 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
% 5.42/1.80 % (3512718)Detected formulas, will run a generic FOF schedule.
% 5.42/1.80 % (3512729)dis-21_1_sil=8000:lcm=predicate:random_seed=3732627136: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)
% 5.42/1.80 % (3512729)Refutation not found, incomplete strategy
% 5.42/1.80 % (3512729)------------------------------
% 5.42/1.80 % (3512729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.80 % (3512729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.80 % (3512729)CaDiCaL version: 2.1.3
% 5.42/1.80 % (3512729)Termination reason: Refutation not found, incomplete strategy
% 5.42/1.80 % (3512729)Time elapsed: 0.002 s
% 5.42/1.80 % (3512729)Peak memory usage: 88 MB
% 5.42/1.80 % (3512729)Instructions burned: 2 (million)
% 5.42/1.80 % (3512728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3831413418:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.42/1.80 % (3512725)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=2934009504:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.42/1.80 % (3512723)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=2474101213:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.42/1.80 % (3512727)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3762651423:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.42/1.80 % (3512724)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=1452933631:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.42/1.80 % (3512726)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4016358984:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.42/1.80 % (3512728)First to succeed.
% 5.42/1.80 % (3512726)Instruction limit reached!
% 5.42/1.80 % (3512726)------------------------------
% 5.42/1.80 % (3512726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.80 % (3512726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.80 % (3512726)CaDiCaL version: 2.1.3
% 5.42/1.80 % (3512726)Termination reason: Instruction limit
% 5.42/1.80 % (3512726)Termination phase: Saturation
% 5.42/1.80 % (3512726)Time elapsed: 0.101 s
% 5.42/1.80 % (3512726)Peak memory usage: 89 MB
% 5.42/1.80 % (3512726)Instructions burned: 109 (million)
% 5.42/1.80 % (3512728)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3512718"
% 5.42/1.80 % (3512727)Instruction limit reached!
% 5.42/1.80 % (3512727)------------------------------
% 5.42/1.80 % (3512727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.80 % (3512727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.80 % (3512727)CaDiCaL version: 2.1.3
% 5.42/1.80 % (3512727)Termination reason: Instruction limit
% 5.42/1.80 % (3512727)Termination phase: Saturation
% 5.42/1.80 % (3512727)Time elapsed: 0.110 s
% 5.42/1.80 % (3512727)Peak memory usage: 89 MB
% 5.42/1.80 % (3512727)Instructions burned: 119 (million)
% 5.42/1.80 % (3512729)------------------------------
% 5.42/1.80 % (3512729)------------------------------
% 5.42/1.80 % (3512737)lrs+10_1_sil=8000:sp=occurrence:random_seed=2412227526:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.42/1.80 % (3512737)Also succeeded, but the first one will report.
% 5.42/1.80 % (3512738)lrs+10_1_sil=32000:urr=on:br=off:random_seed=686534485:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.42/1.80 % (3512739)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3326793710:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 5.42/1.80 % (3512739)Also succeeded, but the first one will report.
% 5.42/1.80 % (3512728)Refutation found. Thanks to Tanya!
% 5.42/1.80 % SZS status Theorem for theBenchmark
% 5.42/1.80 % SZS output start Proof for theBenchmark
% See solution above
% 6.40/2.10 % (3512728)------------------------------
% 6.40/2.10 % (3512728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/2.10 % (3512728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/2.10 % (3512728)CaDiCaL version: 2.1.3
% 6.40/2.10 % (3512728)Termination reason: Refutation
% 6.40/2.10 % (3512728)Time elapsed: 0.109 s
% 6.40/2.10 % (3512728)Peak memory usage: 90 MB
% 6.40/2.10 % (3512728)Instructions burned: 110 (million)
% 6.40/2.10 % (3512728)------------------------------
% 6.40/2.10 % (3512728)------------------------------
% 6.40/2.10 % (3512718)Success in time 0.787 s
% 6.40/2.10 % Vampire exiting
%------------------------------------------------------------------------------