%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE150+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 : n002.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 11:40:29 AM UTC 2026
% Result : Theorem 6.82s 2.43s
% Output : Refutation 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f19,conjecture,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] : strong_iteration(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
? [X0] : strong_iteration(multiplication(X0,zero)) != addition(one,multiplication(X0,zero)),
inference(ennf_transformation,[],[f20]) ).
fof(f26,plain,
strong_iteration(multiplication(sK0,zero)) != addition(one,multiplication(sK0,zero)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f46,plain,
strong_iteration(multiplication(sK0,zero)) != addition(one,multiplication(sK0,zero)),
inference(cnf_transformation,[],[f26]) ).
fof(f64,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[],[f41,f27]) ).
fof(f103,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),
inference(superposition,[],[f37,f31]) ).
fof(f104,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(superposition,[],[f64,f31]) ).
fof(f1763,plain,
! [X0] : addition(one,multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(superposition,[],[f103,f36]) ).
fof(f1830,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(superposition,[],[f104,f36]) ).
fof(f2851,plain,
strong_iteration(multiplication(sK0,zero)) != star(multiplication(sK0,zero)),
inference(superposition,[],[f46,f1763]) ).
fof(f2893,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(forward_demodulation,[],[f1830,f1763]) ).
fof(f2900,plain,
star(multiplication(sK0,zero)) != star(multiplication(sK0,zero)),
inference(superposition,[],[f2851,f2893]) ).
fof(f2912,plain,
$false,
inference(trivial_inequality_removal,[],[f2900]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE150+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n002.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 27 13:15:36 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 6.82/2.43 % (3521749)Detected formulas, will run a generic FOF schedule.
% 6.82/2.43 % (3521757)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2689160369:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.82/2.43 % (3521757)Refutation not found, incomplete strategy
% 6.82/2.43 % (3521757)------------------------------
% 6.82/2.43 % (3521757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.43 % (3521757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.43 % (3521757)CaDiCaL version: 2.1.3
% 6.82/2.43 % (3521757)Termination reason: Refutation not found, incomplete strategy
% 6.82/2.43 % (3521757)Time elapsed: 0.001 s
% 6.82/2.43 % (3521757)Peak memory usage: 88 MB
% 6.82/2.43 % (3521757)Instructions burned: 1 (million)
% 6.82/2.43 % (3521754)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=2312713102:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.82/2.43 % (3521755)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=2230384584:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.82/2.43 % (3521756)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=2194704151:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.82/2.43 % (3521760)dis-21_1_sil=8000:lcm=predicate:random_seed=2673089238: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)
% 6.82/2.43 % (3521758)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=964756347:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.82/2.43 % (3521759)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1774372324:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.82/2.43 % (3521760)Refutation not found, incomplete strategy
% 6.82/2.43 % (3521760)------------------------------
% 6.82/2.43 % (3521760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.43 % (3521760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.43 % (3521760)CaDiCaL version: 2.1.3
% 6.82/2.43 % (3521760)Termination reason: Refutation not found, incomplete strategy
% 6.82/2.43 % (3521760)Time elapsed: 0.003 s
% 6.82/2.43 % (3521760)Peak memory usage: 88 MB
% 6.82/2.43 % (3521760)Instructions burned: 1 (million)
% 6.82/2.43 % (3521759)First to succeed.
% 6.82/2.43 % (3521759)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3521749"
% 6.82/2.43 % (3521758)Instruction limit reached!
% 6.82/2.43 % (3521758)------------------------------
% 6.82/2.43 % (3521758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.43 % (3521758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.43 % (3521758)CaDiCaL version: 2.1.3
% 6.82/2.43 % (3521758)Termination reason: Instruction limit
% 6.82/2.43 % (3521758)Termination phase: Saturation
% 6.82/2.43 % (3521758)Time elapsed: 0.118 s
% 6.82/2.43 % (3521758)Peak memory usage: 89 MB
% 6.82/2.43 % (3521758)Instructions burned: 120 (million)
% 6.82/2.43 % (3521757)------------------------------
% 6.82/2.43 % (3521757)------------------------------
% 6.82/2.43 % (3521769)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2970244110:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 6.82/2.43 % (3521760)------------------------------
% 6.82/2.43 % (3521760)------------------------------
% 6.82/2.43 % (3521768)lrs+10_1_sil=8000:sp=occurrence:random_seed=1270587246:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 6.82/2.43 % (3521769)Also succeeded, but the first one will report.
% 6.82/2.43 % (3521759)Refutation found. Thanks to Tanya!
% 6.82/2.43 % SZS status Theorem for theBenchmark
% 6.82/2.43 % SZS output start Proof for theBenchmark
% See solution above
% 6.82/2.43 % (3521759)------------------------------
% 6.82/2.43 % (3521759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/2.43 % (3521759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/2.43 % (3521759)CaDiCaL version: 2.1.3
% 6.82/2.43 % (3521759)Termination reason: Refutation
% 6.82/2.43 % (3521759)Time elapsed: 0.093 s
% 6.82/2.43 % (3521759)Peak memory usage: 90 MB
% 6.82/2.43 % (3521759)Instructions burned: 98 (million)
% 6.82/2.43 % (3521759)------------------------------
% 6.82/2.43 % (3521759)------------------------------
% 6.82/2.43 % (3521749)Success in time 0.801 s
% 6.82/2.43 % Vampire exiting
%------------------------------------------------------------------------------