%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV191+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:08:21 PM UTC 2026
% Result : Theorem 0.84s 0.96s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 220 ( 151 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 215 ( 31 ~; 22 |; 154 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 40 ( 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f53,conjecture,
( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use )
=> ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,tptp_minus_1) )
=> a_select3(z_defuse,X0,X1) = use ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0002) ).
fof(f54,negated_conjecture,
~ ( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use )
=> ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,tptp_minus_1) )
=> a_select3(z_defuse,X0,X1) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f58,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f78,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n0) )
=> X0 = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f87,plain,
( ? [X0,X1] :
( use != a_select3(z_defuse,X0,X1)
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,tptp_minus_1) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use ),
inference(ennf_transformation,[],[f54]) ).
fof(f88,plain,
( ? [X0,X1] :
( use != a_select3(z_defuse,X0,X1)
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,tptp_minus_1) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f90,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f92,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f91]) ).
fof(f105,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f110,plain,
( use != a_select3(z_defuse,sK0,sK1)
& leq(n0,sK0)
& leq(n0,sK1)
& leq(sK0,n2)
& leq(sK1,tptp_minus_1)
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f88]) ).
fof(f112,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f140,plain,
leq(sK1,tptp_minus_1),
inference(cnf_transformation,[],[f110]) ).
fof(f142,plain,
leq(n0,sK1),
inference(cnf_transformation,[],[f110]) ).
fof(f145,plain,
! [X0] :
( ~ leq(n0,X0)
| n0 = X0
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f146,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f151,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f58]) ).
fof(f154,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f181,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f182,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f188,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f210,plain,
! [X0] : ~ leq(succ(X0),X0),
inference(resolution,[],[f188,f182]) ).
fof(f218,plain,
~ leq(n0,tptp_minus_1),
inference(superposition,[],[f210,f154]) ).
fof(f282,plain,
( ~ leq(sK1,n0)
| n0 = sK1 ),
inference(resolution,[],[f145,f142]) ).
fof(f301,plain,
! [X0] :
( ~ leq(sK1,X0)
| ~ leq(X0,n0)
| n0 = sK1 ),
inference(resolution,[],[f146,f282]) ).
fof(f386,plain,
( ~ leq(tptp_minus_1,n0)
| n0 = sK1 ),
inference(resolution,[],[f301,f140]) ).
fof(f392,plain,
( n0 = sK1
| ~ gt(n0,tptp_minus_1) ),
inference(resolution,[],[f386,f181]) ).
fof(f393,plain,
n0 = sK1,
inference(forward_subsumption_resolution,[],[f392,f151]) ).
fof(f423,plain,
~ leq(sK1,tptp_minus_1),
inference(superposition,[],[f218,f393]) ).
fof(f431,plain,
$false,
inference(forward_subsumption_resolution,[],[f423,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV191+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 10:09:19 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.84/0.96 % (71948)Detected formulas, will run a generic FOF schedule.
% 0.84/0.96 % (71957)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3037892539:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.84/0.96 % (71957)First to succeed.
% 0.84/0.96 % (71957)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-71948"
% 0.84/0.96 % (71954)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=2937753746:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.84/0.96 % (71958)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=867899899:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.84/0.96 % (71955)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=1392893188:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.84/0.96 % (71956)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=466760650:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.84/0.96 % (71953)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=1687776399:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.84/0.96 % (71959)dis-21_1_sil=8000:lcm=predicate:random_seed=811846539: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)
% 0.84/0.96 % (71958)Also succeeded, but the first one will report.
% 0.84/0.96 % (71956)Instruction limit reached!
% 0.84/0.96 % (71956)------------------------------
% 0.84/0.96 % (71956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.84/0.96 % (71956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.96 % (71956)CaDiCaL version: 2.1.3
% 0.84/0.96 % (71956)Termination reason: Instruction limit
% 0.84/0.96 % (71956)Termination phase: Saturation
% 0.84/0.96 % (71956)Time elapsed: 0.053 s
% 0.84/0.96 % (71956)Peak memory usage: 88 MB
% 0.84/0.96 % (71956)Instructions burned: 109 (million)
% 0.84/0.96 % (71959)Instruction limit reached!
% 0.84/0.96 % (71959)------------------------------
% 0.84/0.96 % (71959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.84/0.96 % (71959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.96 % (71959)CaDiCaL version: 2.1.3
% 0.84/0.96 % (71959)Termination reason: Instruction limit
% 0.84/0.96 % (71959)Termination phase: Saturation
% 0.84/0.96 % (71959)Time elapsed: 0.076 s
% 0.84/0.96 % (71959)Peak memory usage: 88 MB
% 0.84/0.96 % (71959)Instructions burned: 130 (million)
% 0.84/0.96 % (71957)Refutation found. Thanks to Tanya!
% 0.84/0.96 % SZS status Theorem for theBenchmark
% 0.84/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.06 % (71957)------------------------------
% 2.65/1.06 % (71957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.06 % (71957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.06 % (71957)CaDiCaL version: 2.1.3
% 2.65/1.06 % (71957)Termination reason: Refutation
% 2.65/1.06 % (71957)Time elapsed: 0.005 s
% 2.65/1.06 % (71957)Peak memory usage: 88 MB
% 2.65/1.06 % (71957)Instructions burned: 14 (million)
% 2.65/1.06 % (71957)------------------------------
% 2.65/1.06 % (71957)------------------------------
% 2.65/1.06 % (71948)Success in time 0.3 s
% 2.65/1.06 % Vampire exiting
%------------------------------------------------------------------------------