%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV198+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Sun Sep 27 09:07:01 AM UTC 2026
% Result : Theorem 49.54s 12.74s
% Output : CNFRefutation 49.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 18 unt; 0 def)
% Number of atoms : 253 ( 169 equ)
% Maximal formula atoms : 45 ( 6 avg)
% Number of connectives : 252 ( 39 ~; 49 |; 154 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 18 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
fof(finite_domain_2,axiom,
! [X] :
( ( leq(X,n2)
& leq(n0,X) )
=> ( X = n2
| X = n1
| X = n0 ) ),
file('theBenchmark.p',finite_domain_2) ).
fof(quaternion_ds1_inuse_0009,conjecture,
( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [E,F] :
( ( leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(u_defuse,E,F) = use ) ),
file('theBenchmark.p',quaternion_ds1_inuse_0009) ).
fof(quaternion_ds1_inuse_0009_neg,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [E,F] :
( ( leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(u_defuse,E,F) = use ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0009]) ).
cnf(c_359,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
cnf(c_361,plain,
( n2 = A
| n1 = A
| n0 = A
| ~ leq(A,n2)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_2]) ).
fof(nnf_56,plain,
( ? [E,F] :
( a_select3(u_defuse,E,F) != use
& leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(fof_nnf,[status(thm)],[quaternion_ds1_inuse_0009_neg]) ).
fof(sk_quaternion_ds1_inuse_0009_neg,plain,
( a_select3(u_defuse,sK0,sK1) != use
& leq(sK1,pv5)
& leq(sK0,n2)
& leq(n0,sK1)
& leq(n0,sK0)
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0),skolemize(F,sK1)],[nnf_56]) ).
cnf(c_382,negated_conjecture,
a_select3(u_defuse,n0,n0) = use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_383,negated_conjecture,
a_select3(u_defuse,n1,n0) = use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_384,negated_conjecture,
a_select3(u_defuse,n2,n0) = use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_400,negated_conjecture,
leq(n0,pv5),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_401,negated_conjecture,
leq(pv5,n0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_407,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_408,negated_conjecture,
leq(n0,sK1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_409,negated_conjecture,
leq(sK0,n2),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_410,negated_conjecture,
leq(sK1,pv5),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_411,negated_conjecture,
a_select3(u_defuse,sK0,sK1) != use,
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_inuse_0009_neg]) ).
cnf(c_13857,negated_conjecture,
( n0 = pv5
| ~ leq(pv5,n0) ),
inference(resolve,[status(thm)],[c_400,c_359]) ).
cnf(c_13858,negated_conjecture,
( pv5 = n0
| ~ leq(pv5,n0) ),
inference(copy,[status(thm)],[c_13857]) ).
cnf(c_1462,negated_conjecture,
pv5 = n0,
inference(resolve,[status(thm)],[c_401,c_13858]) ).
cnf(c_1469,negated_conjecture,
leq(sK1,n0),
inference(paramod,[status(thm)],[c_1462,c_410]) ).
cnf(c_13859,negated_conjecture,
( n2 = sK0
| n1 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(resolve,[status(thm)],[c_407,c_361]) ).
cnf(c_13860,negated_conjecture,
( n2 = sK0
| n1 = sK0
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_13859]) ).
cnf(c_13861,negated_conjecture,
( n2 = sK0
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_13860]) ).
cnf(c_13862,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0
| ~ leq(sK0,n2) ),
inference(copy,[status(thm)],[c_13861]) ).
cnf(c_1473,negated_conjecture,
( sK0 = n2
| sK0 = n1
| sK0 = n0 ),
inference(resolve,[status(thm)],[c_409,c_13862]) ).
cnf(c_13863,negated_conjecture,
( n0 = sK1
| ~ leq(sK1,n0) ),
inference(resolve,[status(thm)],[c_408,c_359]) ).
cnf(c_13864,negated_conjecture,
( sK1 = n0
| ~ leq(sK1,n0) ),
inference(copy,[status(thm)],[c_13863]) ).
cnf(c_1848,negated_conjecture,
sK1 = n0,
inference(resolve,[status(thm)],[c_1469,c_13864]) ).
cnf(c_1849,negated_conjecture,
a_select3(u_defuse,sK0,n0) != use,
inference(paramod,[status(thm)],[c_1848,c_411]) ).
cnf(c_13865,plain,
( a_select3(u_defuse,n1,n0) != use
| sK0 = n2
| sK0 = n0 ),
inference(paramod,[status(thm)],[c_1473,c_1849]) ).
cnf(c_13866,plain,
( use != use
| sK0 = n2
| sK0 = n0 ),
inference(paramod,[status(thm)],[c_383,c_13865]) ).
cnf(c_13852,plain,
( sK0 = n2
| sK0 = n0 ),
inference(copy,[status(thm)],[c_13866]) ).
cnf(c_13867,plain,
( a_select3(u_defuse,n2,n0) != use
| sK0 = n0 ),
inference(paramod,[status(thm)],[c_13852,c_1849]) ).
cnf(c_13868,plain,
( use != use
| sK0 = n0 ),
inference(paramod,[status(thm)],[c_384,c_13867]) ).
cnf(c_13855,plain,
sK0 = n0,
inference(copy,[status(thm)],[c_13868]) ).
cnf(c_13869,negated_conjecture,
a_select3(u_defuse,n0,n0) != use,
inference(paramod,[status(thm)],[c_13855,c_1849]) ).
cnf(c_13870,negated_conjecture,
use != use,
inference(paramod,[status(thm)],[c_382,c_13869]) ).
cnf(c_13856,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_13870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV198+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n011.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 13:19:19 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 648114 was started by sandbox2 on n011,
% 0.16/5.45 % Sat Sep 26 13:19:19 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/5.56
% 0.21/5.56 % From the command line: assign(max_seconds, 300).
% 49.54/12.74
% 49.54/12.74 % given #500 (I,wt=158): 597 leq(n0,f19(A,B,C,D,E,F,V6,V7)) | leq(n0,f21(A,B,C,D,E,F,V6,V7)) | leq(f23(A,B,C,D,E,F,V6,V7),V6) | -leq(n0,V6) | a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),n0,V6) = a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),V6,n0). [factor(154,d,g),unit_del(e,64),unit_del(f,64)].
% 49.54/12.74
% 49.54/12.74 % given #1000 (A,wt=46): 987 leq(n0,f5(A,B)) | -leq(n0,B) | -leq(n0,C) | -leq(C,B) | a_select3(tptp_update3(A,B,B,D),C,B) = a_select3(tptp_update3(A,B,B,D),B,C). [factor(981,b,e),unit_del(e,64)].
% 49.54/12.74
% 49.54/12.74 % SZS status Theorem for theBenchmark
% 49.54/12.74
% 49.54/12.74 % Proof 1 at 5.95 (+ 1.09) seconds.
% 49.54/12.74 % Length of proof is 23.
% 49.54/12.74 % Level of proof is 8.
% 49.54/12.74 % Maximum clause weight is 20.000.
% 49.54/12.74 % Given clauses 1110.
% 49.54/12.74
% 49.54/12.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------