%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE093+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 : n013.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 11:40:19 AM UTC 2026
% Result : Theorem 3.91s 1.52s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 38 unt; 0 def)
% Number of atoms : 46 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 52 !; 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(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
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(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f17,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f19,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f21,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
fof(f22,conjecture,
! [X0] : domain(star(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f23,negated_conjecture,
~ ! [X0] : domain(star(X0)) = one,
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f26,plain,
? [X0] : one != domain(star(X0)),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f28,plain,
one != domain(star(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f26]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f46,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f19]) ).
fof(f50,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
one != domain(star(sK0)),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0] : one = addition(one,domain(X0)),
inference(superposition,[],[f29,f48]) ).
fof(f66,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f42,f40]) ).
fof(f70,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f66,f29]) ).
fof(f111,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f30,f29]) ).
fof(f139,plain,
domain(one) = addition(one,domain(one)),
inference(superposition,[],[f46,f34]) ).
fof(f144,plain,
one = domain(one),
inference(forward_demodulation,[],[f139,f54]) ).
fof(f148,plain,
! [X0] : addition(one,domain(X0)) = domain(addition(one,X0)),
inference(superposition,[],[f50,f144]) ).
fof(f150,plain,
! [X0] : one = domain(addition(one,X0)),
inference(forward_demodulation,[],[f148,f54]) ).
fof(f190,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f37,f35]) ).
fof(f1187,plain,
! [X0] : star(X0) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(forward_demodulation,[],[f70,f111]) ).
fof(f1188,plain,
! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f1187,f29]) ).
fof(f1189,plain,
! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[],[f1188,f190]) ).
fof(f1240,plain,
! [X0] : one = domain(star(X0)),
inference(superposition,[],[f150,f1189]) ).
fof(f1278,plain,
one != one,
inference(superposition,[],[f51,f1240]) ).
fof(f1293,plain,
$false,
inference(trivial_inequality_removal,[],[f1278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE093+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 : n013.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 13:09:07 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
% 3.91/1.52 % (215418)Detected formulas, will run a generic FOF schedule.
% 3.91/1.52 % (215425)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=2113367887:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.91/1.52 % (215428)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1226403140:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.91/1.52 % (215426)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2778208343:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.91/1.52 % (215429)dis-21_1_sil=8000:lcm=predicate:random_seed=1529905118: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)
% 3.91/1.52 % (215423)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=3182395531:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.91/1.52 % (215427)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1484001201:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.91/1.52 % (215424)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=1011469425:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.91/1.52 % (215426)Refutation not found, incomplete strategy
% 3.91/1.52 % (215426)------------------------------
% 3.91/1.52 % (215426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.52 % (215426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.52 % (215426)CaDiCaL version: 2.1.3
% 3.91/1.52 % (215426)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.52 % (215426)Time elapsed: 0.001 s
% 3.91/1.52 % (215426)Peak memory usage: 88 MB
% 3.91/1.52 % (215429)Refutation not found, incomplete strategy
% 3.91/1.52 % (215429)------------------------------
% 3.91/1.52 % (215429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.52 % (215429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.52 % (215429)CaDiCaL version: 2.1.3
% 3.91/1.52 % (215429)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.52 % (215429)Time elapsed: 0.002 s
% 3.91/1.52 % (215429)Peak memory usage: 88 MB
% 3.91/1.52 % (215429)Instructions burned: 1 (million)
% 3.91/1.52 % (215428)First to succeed.
% 3.91/1.52 % (215428)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-215418"
% 3.91/1.52 % (215427)Also succeeded, but the first one will report.
% 3.91/1.52 % (215426)------------------------------
% 3.91/1.52 % (215426)------------------------------
% 3.91/1.52 % (215429)------------------------------
% 3.91/1.52 % (215429)------------------------------
% 3.91/1.52 % (215428)Refutation found. Thanks to Tanya!
% 3.91/1.52 % SZS status Theorem for theBenchmark
% 3.91/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.52 % (215428)------------------------------
% 3.91/1.52 % (215428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.52 % (215428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.52 % (215428)CaDiCaL version: 2.1.3
% 3.91/1.52 % (215428)Termination reason: Refutation
% 3.91/1.52 % (215428)Time elapsed: 0.026 s
% 3.91/1.52 % (215428)Peak memory usage: 89 MB
% 3.91/1.52 % (215428)Instructions burned: 41 (million)
% 3.91/1.52 % (215428)------------------------------
% 3.91/1.52 % (215428)------------------------------
% 3.91/1.52 % (215418)Success in time 0.465 s
% 3.91/1.52 % Vampire exiting
%------------------------------------------------------------------------------