%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE085+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 : n001.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 11:40:17 AM UTC 2026
% Result : Theorem 4.90s 1.73s
% Output : Refutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 23 !; 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(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
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(f21,conjecture,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0] : addition(domain(X0),one) = one,
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0] : one != addition(domain(X0),one),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
one != addition(domain(sK0),one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f25,plain,
one != addition(domain(sK0),one),
inference(cnf_transformation,[],[f24]) ).
fof(f26,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f41,plain,
one != addition(antidomain(antidomain(sK0)),one),
inference(definition_unfolding,[],[f25,f31]) ).
fof(f46,plain,
one != addition(one,antidomain(antidomain(sK0))),
inference(superposition,[],[f41,f28]) ).
fof(f50,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f35,f28]) ).
fof(f57,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f27,f26]) ).
fof(f232,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(superposition,[],[f57,f50]) ).
fof(f240,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[],[f232,f28]) ).
fof(f282,plain,
one != one,
inference(superposition,[],[f46,f240]) ).
fof(f285,plain,
$false,
inference(trivial_inequality_removal,[],[f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 13:15:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 4.90/1.72 % (3559436)Detected formulas, will run a generic FOF schedule.
% 4.90/1.72 % (3559463)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3739987662:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.90/1.72 % (3559466)dis-21_1_sil=8000:lcm=predicate:random_seed=119271084: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)
% 4.90/1.72 % (3559463)Refutation not found, incomplete strategy
% 4.90/1.72 % (3559463)------------------------------
% 4.90/1.72 % (3559463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/1.72 % (3559463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/1.72 % (3559463)CaDiCaL version: 2.1.3
% 4.90/1.72 % (3559463)Termination reason: Refutation not found, incomplete strategy
% 4.90/1.72 % (3559463)Time elapsed: 0.001 s
% 4.90/1.72 % (3559463)Peak memory usage: 88 MB
% 4.90/1.72 % (3559466)Refutation not found, incomplete strategy
% 4.90/1.72 % (3559466)------------------------------
% 4.90/1.72 % (3559466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/1.72 % (3559466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/1.72 % (3559466)CaDiCaL version: 2.1.3
% 4.90/1.72 % (3559466)Termination reason: Refutation not found, incomplete strategy
% 4.90/1.72 % (3559466)Time elapsed: 0.002 s
% 4.90/1.72 % (3559466)Peak memory usage: 88 MB
% 4.90/1.72 % (3559466)Instructions burned: 1 (million)
% 4.90/1.72 % (3559462)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=4178326073:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.90/1.72 % (3559464)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1139769364:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.90/1.72 % (3559464)First to succeed.
% 4.90/1.72 % (3559464)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3559436"
% 4.90/1.72 % (3559465)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1406621041:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.90/1.72 % (3559460)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=2914259577:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.90/1.73 % (3559465)Also succeeded, but the first one will report.
% 4.90/1.73 % (3559461)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=2287716540:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.90/1.73 % (3559463)------------------------------
% 4.90/1.73 % (3559463)------------------------------
% 4.90/1.73 % (3559479)lrs+10_1_sil=8000:sp=occurrence:random_seed=1665741402:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.90/1.73 % (3559466)------------------------------
% 4.90/1.73 % (3559466)------------------------------
% 4.90/1.73 % (3559479)Also succeeded, but the first one will report.
% 4.90/1.73 % (3559464)Refutation found. Thanks to Tanya!
% 4.90/1.73 % SZS status Theorem for theBenchmark
% 4.90/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 4.90/1.73 % (3559464)------------------------------
% 4.90/1.73 % (3559464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/1.73 % (3559464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/1.73 % (3559464)CaDiCaL version: 2.1.3
% 4.90/1.73 % (3559464)Termination reason: Refutation
% 4.90/1.73 % (3559464)Time elapsed: 0.011 s
% 4.90/1.73 % (3559464)Peak memory usage: 88 MB
% 4.90/1.73 % (3559464)Instructions burned: 9 (million)
% 4.90/1.73 % (3559464)------------------------------
% 4.90/1.73 % (3559464)------------------------------
% 4.90/1.73 % (3559436)Success in time 0.587 s
% 4.90/1.73 % Vampire exiting
%------------------------------------------------------------------------------