%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE128+1 : 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 : n015.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 11:40:24 AM UTC 2026
% Result : Theorem 5.42s 2.08s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 47 unt; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 7 ~; 3 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 57 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
fof(f28,axiom,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2))
=> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence2) ).
fof(f29,conjecture,
! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f32,plain,
? [X0] :
( ? [X1] :
( zero != domain(X1)
& addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1)) )
& divergence(X0) = zero ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
( zero != domain(sK1)
& forward_diamond(sK0,domain(sK1)) = addition(domain(sK1),forward_diamond(sK0,domain(sK1)))
& zero = divergence(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(f40,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
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(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(f60,plain,
! [X2,X0,X1] :
( addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2)))
| addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) ),
inference(cnf_transformation,[],[f31]) ).
fof(f61,plain,
zero = divergence(sK0),
inference(cnf_transformation,[],[f33]) ).
fof(f62,plain,
forward_diamond(sK0,domain(sK1)) = addition(domain(sK1),forward_diamond(sK0,domain(sK1))),
inference(cnf_transformation,[],[f33]) ).
fof(f63,plain,
zero != domain(sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f73,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f34,f36]) ).
fof(f77,plain,
zero = forward_diamond(sK0,zero),
inference(superposition,[],[f59,f61]) ).
fof(f78,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f47,f34]) ).
fof(f79,plain,
! [X0] : one = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[],[f78,f48]) ).
fof(f80,plain,
! [X0] : one = addition(domain(X0),antidomain(X0)),
inference(forward_demodulation,[],[f79,f34]) ).
fof(f102,plain,
! [X0,X1] : one = addition(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))),
inference(superposition,[],[f80,f55]) ).
fof(f110,plain,
! [X0] : addition(forward_diamond(sK0,domain(sK1)),X0) = addition(domain(sK1),addition(forward_diamond(sK0,domain(sK1)),X0)),
inference(superposition,[],[f35,f62]) ).
fof(f338,plain,
! [X0] :
( addition(forward_diamond(sK0,domain(sK1)),domain(X0)) != addition(forward_diamond(sK0,domain(sK1)),domain(X0))
| addition(divergence(sK0),forward_diamond(star(sK0),domain(X0))) = addition(domain(sK1),addition(divergence(sK0),forward_diamond(star(sK0),domain(X0)))) ),
inference(superposition,[],[f60,f110]) ).
fof(f339,plain,
! [X0] : addition(divergence(sK0),forward_diamond(star(sK0),domain(X0))) = addition(domain(sK1),addition(divergence(sK0),forward_diamond(star(sK0),domain(X0)))),
inference(trivial_inequality_removal,[],[f338]) ).
fof(f340,plain,
! [X0] : addition(zero,forward_diamond(star(sK0),domain(X0))) = addition(domain(sK1),addition(zero,forward_diamond(star(sK0),domain(X0)))),
inference(forward_demodulation,[],[f339,f61]) ).
fof(f342,plain,
! [X0] : forward_diamond(star(sK0),domain(X0)) = addition(domain(sK1),forward_diamond(star(sK0),domain(X0))),
inference(forward_demodulation,[],[f340,f73]) ).
fof(f344,plain,
! [X0,X1] : forward_diamond(star(sK0),forward_diamond(X0,X1)) = addition(domain(sK1),forward_diamond(star(sK0),forward_diamond(X0,X1))),
inference(superposition,[],[f342,f55]) ).
fof(f351,plain,
forward_diamond(star(sK0),zero) = addition(domain(sK1),forward_diamond(star(sK0),zero)),
inference(superposition,[],[f344,f77]) ).
fof(f864,plain,
one = addition(zero,antidomain(multiplication(sK0,domain(zero)))),
inference(superposition,[],[f102,f77]) ).
fof(f896,plain,
one = antidomain(multiplication(sK0,domain(zero))),
inference(forward_demodulation,[],[f864,f73]) ).
fof(f1619,plain,
zero = multiplication(one,multiplication(sK0,domain(zero))),
inference(superposition,[],[f45,f896]) ).
fof(f1638,plain,
zero = multiplication(sK0,domain(zero)),
inference(forward_demodulation,[],[f1619,f40]) ).
fof(f1659,plain,
forward_diamond(sK0,zero) = domain(zero),
inference(superposition,[],[f55,f1638]) ).
fof(f1676,plain,
zero = domain(zero),
inference(forward_demodulation,[],[f1659,f77]) ).
fof(f1708,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(superposition,[],[f55,f1676]) ).
fof(f1727,plain,
! [X0] : domain(zero) = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f1708,f43]) ).
fof(f1732,plain,
! [X0] : zero = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f1727,f1676]) ).
fof(f2079,plain,
zero = addition(domain(sK1),zero),
inference(superposition,[],[f351,f1732]) ).
fof(f2080,plain,
zero = domain(sK1),
inference(forward_demodulation,[],[f2079,f36]) ).
fof(f2086,plain,
$false,
inference(forward_subsumption_resolution,[],[f2080,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 % Computer : n015.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sun Sep 27 13:15:00 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.54 Running first-order theorem proving
% 0.27/0.54 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
% 5.42/2.08 % (1667120)Detected formulas, will run a generic FOF schedule.
% 5.42/2.08 % (1667134)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=3875150096:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.42/2.08 % (1667135)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=4080554503:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.42/2.08 % (1667133)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=2707428107:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.42/2.08 % (1667136)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2657840723:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.42/2.08 % (1667137)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4204316371:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.42/2.08 % (1667138)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=287473598:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.42/2.08 % (1667139)dis-21_1_sil=8000:lcm=predicate:random_seed=2062950002: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)
% 5.42/2.08 % (1667139)Refutation not found, incomplete strategy
% 5.42/2.08 % (1667139)------------------------------
% 5.42/2.08 % (1667139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/2.08 % (1667139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/2.08 % (1667139)CaDiCaL version: 2.1.3
% 5.42/2.08 % (1667139)Termination reason: Refutation not found, incomplete strategy
% 5.42/2.08 % (1667139)Time elapsed: 0.004 s
% 5.42/2.08 % (1667139)Peak memory usage: 88 MB
% 5.42/2.08 % (1667139)Instructions burned: 2 (million)
% 5.42/2.08 % (1667138)First to succeed.
% 5.42/2.08 % (1667138)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1667120"
% 5.42/2.08 % (1667136)Instruction limit reached!
% 5.42/2.08 % (1667136)------------------------------
% 5.42/2.08 % (1667136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/2.08 % (1667136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/2.08 % (1667136)CaDiCaL version: 2.1.3
% 5.42/2.08 % (1667136)Termination reason: Instruction limit
% 5.42/2.08 % (1667136)Termination phase: Saturation
% 5.42/2.08 % (1667136)Time elapsed: 0.106 s
% 5.42/2.08 % (1667136)Peak memory usage: 89 MB
% 5.42/2.08 % (1667136)Instructions burned: 109 (million)
% 5.42/2.08 % (1667137)Instruction limit reached!
% 5.42/2.08 % (1667137)------------------------------
% 5.42/2.08 % (1667137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/2.08 % (1667137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/2.08 % (1667137)CaDiCaL version: 2.1.3
% 5.42/2.08 % (1667137)Termination reason: Instruction limit
% 5.42/2.08 % (1667137)Termination phase: Saturation
% 5.42/2.08 % (1667137)Time elapsed: 0.112 s
% 5.42/2.08 % (1667137)Peak memory usage: 88 MB
% 5.42/2.08 % (1667137)Instructions burned: 119 (million)
% 5.42/2.08 % (1667147)lrs+10_1_sil=8000:sp=occurrence:random_seed=3408816409:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 5.42/2.08 % (1667139)------------------------------
% 5.42/2.08 % (1667139)------------------------------
% 5.42/2.08 % (1667148)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2494910614:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 5.42/2.08 % (1667138)Refutation found. Thanks to Tanya!
% 5.42/2.08 % SZS status Theorem for theBenchmark
% 5.42/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/2.40 % (1667138)------------------------------
% 0.31/2.40 % (1667138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/2.40 % (1667138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/2.40 % (1667138)CaDiCaL version: 2.1.3
% 0.31/2.40 % (1667138)Termination reason: Refutation
% 0.31/2.40 % (1667138)Time elapsed: 0.077 s
% 0.31/2.40 % (1667138)Peak memory usage: 89 MB
% 0.31/2.40 % (1667138)Instructions burned: 79 (million)
% 0.31/2.40 % (1667138)------------------------------
% 0.31/2.40 % (1667138)------------------------------
% 0.31/2.40 % (1667120)Success in time 0.777 s
% 0.31/2.41 % Vampire exiting
%------------------------------------------------------------------------------