%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE053+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 : n009.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 11:40:13 AM UTC 2026
% Result : Theorem 3.82s 1.53s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f18,conjecture,
! [X0] : domain(domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] : domain(domain(X0)) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] : domain(X0) != domain(domain(X0)),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
domain(sK0) != domain(domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
fof(f28,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f38,plain,
domain(sK0) != domain(domain(sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f49,plain,
! [X0] : domain(domain(X0)) = domain(multiplication(one,X0)),
inference(superposition,[],[f34,f28]) ).
fof(f52,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[],[f49,f28]) ).
fof(f183,plain,
domain(sK0) != domain(sK0),
inference(superposition,[],[f38,f52]) ).
fof(f189,plain,
$false,
inference(trivial_inequality_removal,[],[f183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE053+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 13:07:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.82/1.53 % (2020766)Detected formulas, will run a generic FOF schedule.
% 3.82/1.53 % (2020774)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3134437655:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.82/1.53 % (2020774)Refutation not found, incomplete strategy
% 3.82/1.53 % (2020774)------------------------------
% 3.82/1.53 % (2020774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.53 % (2020774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.53 % (2020774)CaDiCaL version: 2.1.3
% 3.82/1.53 % (2020774)Termination reason: Refutation not found, incomplete strategy
% 3.82/1.53 % (2020774)Time elapsed: 0.001 s
% 3.82/1.53 % (2020774)Peak memory usage: 88 MB
% 3.82/1.53 % (2020773)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=202072826:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.82/1.53 % (2020771)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=254326786:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.82/1.53 % (2020772)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=1083934863:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.82/1.53 % (2020775)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=557401869:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.82/1.53 % (2020777)dis-21_1_sil=8000:lcm=predicate:random_seed=3177931337: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)
% 3.82/1.53 % (2020776)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2384498785:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.82/1.53 % (2020777)Refutation not found, incomplete strategy
% 3.82/1.53 % (2020777)------------------------------
% 3.82/1.53 % (2020777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.53 % (2020777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.53 % (2020777)CaDiCaL version: 2.1.3
% 3.82/1.53 % (2020777)Termination reason: Refutation not found, incomplete strategy
% 3.82/1.53 % (2020777)Time elapsed: 0.001 s
% 3.82/1.53 % (2020777)Peak memory usage: 88 MB
% 3.82/1.53 % (2020777)Instructions burned: 1 (million)
% 3.82/1.53 % (2020776)First to succeed.
% 3.82/1.53 % (2020776)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2020766"
% 3.82/1.53 % (2020775)Instruction limit reached!
% 3.82/1.53 % (2020775)------------------------------
% 3.82/1.53 % (2020775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.53 % (2020775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.53 % (2020775)CaDiCaL version: 2.1.3
% 3.82/1.53 % (2020775)Termination reason: Instruction limit
% 3.82/1.53 % (2020775)Termination phase: Saturation
% 3.82/1.53 % (2020775)Time elapsed: 0.063 s
% 3.82/1.53 % (2020775)Peak memory usage: 88 MB
% 3.82/1.53 % (2020775)Instructions burned: 121 (million)
% 3.82/1.53 % (2020774)------------------------------
% 3.82/1.53 % (2020774)------------------------------
% 3.82/1.53 % (2020786)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2408695977:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.82/1.53 % (2020785)lrs+10_1_sil=8000:sp=occurrence:random_seed=3879358094:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.82/1.53 % (2020785)Also succeeded, but the first one will report.
% 3.82/1.53 % (2020777)------------------------------
% 3.82/1.53 % (2020777)------------------------------
% 3.82/1.53 % (2020776)Refutation found. Thanks to Tanya!
% 3.82/1.53 % SZS status Theorem for theBenchmark
% 3.82/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.82/1.53 % (2020776)------------------------------
% 3.82/1.53 % (2020776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.53 % (2020776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.53 % (2020776)CaDiCaL version: 2.1.3
% 3.82/1.53 % (2020776)Termination reason: Refutation
% 3.82/1.53 % (2020776)Time elapsed: 0.006 s
% 3.82/1.53 % (2020776)Peak memory usage: 89 MB
% 3.82/1.53 % (2020776)Instructions burned: 7 (million)
% 3.82/1.53 % (2020776)------------------------------
% 3.82/1.53 % (2020776)------------------------------
% 3.82/1.53 % (2020766)Success in time 0.446 s
% 3.82/1.53 % Vampire exiting
%------------------------------------------------------------------------------