%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE061+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 : n008.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 11:40:14 AM UTC 2026
% Result : Theorem 2.77s 1.07s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 32 ( 31 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f18,conjecture,
! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] : domain(X0) != multiplication(domain(X0),domain(X0)),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
domain(sK0) != multiplication(domain(sK0),domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
fof(f22,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f30,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f33,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f34,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f35,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
domain(sK0) != multiplication(domain(sK0),domain(sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X0] : one = addition(one,domain(X0)),
inference(superposition,[],[f22,f35]) ).
fof(f49,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(superposition,[],[f34,f28]) ).
fof(f52,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[],[f49,f28]) ).
fof(f154,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f30,f28]) ).
fof(f893,plain,
! [X0] : multiplication(domain(X0),X0) = multiplication(addition(one,domain(X0)),X0),
inference(superposition,[],[f33,f154]) ).
fof(f920,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[],[f893,f41]) ).
fof(f928,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(forward_demodulation,[],[f920,f28]) ).
fof(f939,plain,
! [X0] : domain(X0) = multiplication(domain(X0),domain(X0)),
inference(superposition,[],[f928,f52]) ).
fof(f1100,plain,
domain(sK0) != domain(sK0),
inference(superposition,[],[f38,f939]) ).
fof(f1113,plain,
$false,
inference(trivial_inequality_removal,[],[f1100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE061+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.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 13:08:54 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 2.77/1.07 % (1209762)Detected formulas, will run a generic FOF schedule.
% 2.77/1.07 % (1209767)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=4214804140:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.07 % (1209773)dis-21_1_sil=8000:lcm=predicate:random_seed=1408539212: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)
% 2.77/1.07 % (1209769)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=1273669025:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.07 % (1209771)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4074263151:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.07 % (1209768)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=3930851367:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.07 % (1209770)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=59624141:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.07 % (1209770)Refutation not found, incomplete strategy
% 2.77/1.07 % (1209770)------------------------------
% 2.77/1.07 % (1209770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.07 % (1209770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.07 % (1209770)CaDiCaL version: 2.1.3
% 2.77/1.07 % (1209770)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.07 % (1209770)Time elapsed: 0.001 s
% 2.77/1.07 % (1209770)Peak memory usage: 88 MB
% 2.77/1.07 % (1209773)Refutation not found, incomplete strategy
% 2.77/1.07 % (1209773)------------------------------
% 2.77/1.07 % (1209773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.07 % (1209773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.07 % (1209773)CaDiCaL version: 2.1.3
% 2.77/1.07 % (1209773)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.07 % (1209773)Time elapsed: 0.001 s
% 2.77/1.07 % (1209773)Peak memory usage: 88 MB
% 2.77/1.07 % (1209773)Instructions burned: 1 (million)
% 2.77/1.07 % (1209772)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=760261630:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.07 % (1209772)First to succeed.
% 2.77/1.07 % (1209772)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1209762"
% 2.77/1.07 % (1209771)Instruction limit reached!
% 2.77/1.07 % (1209771)------------------------------
% 2.77/1.07 % (1209771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.07 % (1209771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.07 % (1209771)CaDiCaL version: 2.1.3
% 2.77/1.07 % (1209771)Termination reason: Instruction limit
% 2.77/1.07 % (1209771)Termination phase: Saturation
% 2.77/1.07 % (1209771)Time elapsed: 0.062 s
% 2.77/1.07 % (1209771)Peak memory usage: 88 MB
% 2.77/1.07 % (1209771)Instructions burned: 120 (million)
% 2.77/1.07 % (1209772)Refutation found. Thanks to Tanya!
% 2.77/1.07 % SZS status Theorem for theBenchmark
% 2.77/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.07 % (1209772)------------------------------
% 2.77/1.07 % (1209772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.07 % (1209772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.07 % (1209772)CaDiCaL version: 2.1.3
% 2.77/1.07 % (1209772)Termination reason: Refutation
% 2.77/1.07 % (1209772)Time elapsed: 0.022 s
% 2.77/1.07 % (1209772)Peak memory usage: 89 MB
% 2.77/1.07 % (1209772)Instructions burned: 34 (million)
% 2.77/1.07 % (1209772)------------------------------
% 2.77/1.07 % (1209772)------------------------------
% 2.77/1.07 % (1209762)Success in time 0.35 s
% 2.77/1.07 % Vampire exiting
%------------------------------------------------------------------------------