%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE054+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 : n016.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 3.93s 1.51s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
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(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
fof(f18,conjecture,
! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] : domain(X0) != addition(domain(multiplication(X0,X1)),domain(X0)),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
domain(sK0) != addition(domain(multiplication(sK0,sK1)),domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
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(f37,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
domain(sK0) != addition(domain(multiplication(sK0,sK1)),domain(sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X0] : one = addition(one,domain(X0)),
inference(superposition,[],[f22,f35]) ).
fof(f59,plain,
! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = addition(domain(X2),domain(multiplication(X0,X1))),
inference(superposition,[],[f37,f34]) ).
fof(f63,plain,
domain(sK0) != domain(addition(multiplication(sK0,sK1),sK0)),
inference(superposition,[],[f38,f37]) ).
fof(f68,plain,
domain(sK0) != domain(addition(sK0,multiplication(sK0,sK1))),
inference(forward_demodulation,[],[f63,f22]) ).
fof(f69,plain,
! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = domain(addition(X2,multiplication(X0,X1))),
inference(forward_demodulation,[],[f59,f37]) ).
fof(f120,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f29,f27]) ).
fof(f813,plain,
domain(sK0) != domain(multiplication(sK0,addition(one,sK1))),
inference(superposition,[],[f68,f120]) ).
fof(f1653,plain,
! [X0,X1] : domain(addition(X0,multiplication(X0,X1))) = domain(multiplication(X0,addition(one,domain(X1)))),
inference(superposition,[],[f69,f120]) ).
fof(f1702,plain,
! [X0,X1] : domain(multiplication(X0,one)) = domain(addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[],[f1653,f41]) ).
fof(f1723,plain,
! [X0,X1] : domain(multiplication(X0,one)) = domain(multiplication(X0,addition(one,X1))),
inference(forward_demodulation,[],[f1702,f120]) ).
fof(f1730,plain,
! [X0,X1] : domain(X0) = domain(multiplication(X0,addition(one,X1))),
inference(forward_demodulation,[],[f1723,f27]) ).
fof(f2375,plain,
domain(sK0) != domain(sK0),
inference(superposition,[],[f813,f1730]) ).
fof(f2393,plain,
$false,
inference(trivial_inequality_removal,[],[f2375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE054+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 13:12:32 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 3.93/1.51 % (2627352)Detected formulas, will run a generic FOF schedule.
% 3.93/1.51 % (2627363)dis-21_1_sil=8000:lcm=predicate:random_seed=1277093246: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)
% 3.93/1.51 % (2627363)Refutation not found, incomplete strategy
% 3.93/1.51 % (2627363)------------------------------
% 3.93/1.51 % (2627363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.51 % (2627363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.51 % (2627363)CaDiCaL version: 2.1.3
% 3.93/1.51 % (2627363)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.51 % (2627363)Time elapsed: 0.001 s
% 3.93/1.51 % (2627363)Peak memory usage: 88 MB
% 3.93/1.51 % (2627363)Instructions burned: 1 (million)
% 3.93/1.51 % (2627362)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1994445558:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.93/1.51 % (2627361)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=888640245:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.93/1.51 % (2627358)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=2759436179:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.93/1.51 % (2627360)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1969105737:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.93/1.51 % (2627357)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=1964597109:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.93/1.51 % (2627359)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=1599404504:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.93/1.51 % (2627360)Refutation not found, incomplete strategy
% 3.93/1.51 % (2627360)------------------------------
% 3.93/1.51 % (2627360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.51 % (2627360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.51 % (2627360)CaDiCaL version: 2.1.3
% 3.93/1.51 % (2627360)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.51 % (2627360)Time elapsed: 0.002 s
% 3.93/1.51 % (2627360)Peak memory usage: 88 MB
% 3.93/1.51 % (2627362)First to succeed.
% 3.93/1.51 % (2627362)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2627352"
% 3.93/1.51 % (2627361)Instruction limit reached!
% 3.93/1.51 % (2627361)------------------------------
% 3.93/1.51 % (2627361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.51 % (2627361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.51 % (2627361)CaDiCaL version: 2.1.3
% 3.93/1.51 % (2627361)Termination reason: Instruction limit
% 3.93/1.51 % (2627361)Termination phase: Saturation
% 3.93/1.51 % (2627361)Time elapsed: 0.064 s
% 3.93/1.51 % (2627361)Peak memory usage: 88 MB
% 3.93/1.51 % (2627361)Instructions burned: 120 (million)
% 3.93/1.51 % (2627363)------------------------------
% 3.93/1.51 % (2627363)------------------------------
% 3.93/1.51 % (2627371)lrs+10_1_sil=8000:sp=occurrence:random_seed=1807765488:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.93/1.51 % (2627360)------------------------------
% 3.93/1.51 % (2627360)------------------------------
% 3.93/1.51 % (2627372)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1413263258:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.93/1.51 % (2627371)Also succeeded, but the first one will report.
% 3.93/1.51 % (2627362)Refutation found. Thanks to Tanya!
% 3.93/1.51 % SZS status Theorem for theBenchmark
% 3.93/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.52 % (2627362)------------------------------
% 3.93/1.52 % (2627362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.52 % (2627362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.52 % (2627362)CaDiCaL version: 2.1.3
% 3.93/1.52 % (2627362)Termination reason: Refutation
% 3.93/1.52 % (2627362)Time elapsed: 0.044 s
% 3.93/1.52 % (2627362)Peak memory usage: 89 MB
% 3.93/1.52 % (2627362)Instructions burned: 74 (million)
% 3.93/1.52 % (2627362)------------------------------
% 3.93/1.52 % (2627362)------------------------------
% 3.93/1.52 % (2627352)Success in time 0.465 s
% 3.93/1.52 % Vampire exiting
%------------------------------------------------------------------------------