%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV193+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 09:07:00 AM UTC 2026
% Result : Theorem 2.45s 0.77s
% Output : CNFRefutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 122 ( 77 equ)
% Maximal formula atoms : 52 ( 8 avg)
% Number of connectives : 121 ( 13 ~; 4 |; 93 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X),
file('theBenchmark.p',irreflexivity_gt) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
fof(quaternion_ds1_inuse_0004,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 )
& gt(pv5,n0)
& 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,pred(pv5))
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(z_defuse,E,F) = use ) ) ),
file('theBenchmark.p',quaternion_ds1_inuse_0004) ).
fof(quaternion_ds1_inuse_0004_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 )
& gt(pv5,n0)
& 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,pred(pv5))
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(z_defuse,E,F) = use ) ) ),
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0004]) ).
cnf(c_63,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[irreflexivity_gt]) ).
cnf(c_359,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
cnf(c_400,negated_conjecture,
leq(n0,pv5),
inference(clausify,[status(thm)],[quaternion_ds1_inuse_0004_neg]) ).
cnf(c_401,negated_conjecture,
leq(pv5,n0),
inference(clausify,[status(thm)],[quaternion_ds1_inuse_0004_neg]) ).
cnf(c_403,negated_conjecture,
gt(pv5,n0),
inference(clausify,[status(thm)],[quaternion_ds1_inuse_0004_neg]) ).
cnf(c_1366,negated_conjecture,
( n0 = pv5
| ~ leq(pv5,n0) ),
inference(resolve,[status(thm)],[c_400,c_359]) ).
cnf(c_1367,negated_conjecture,
( pv5 = n0
| ~ leq(pv5,n0) ),
inference(copy,[status(thm)],[c_1366]) ).
cnf(c_1350,negated_conjecture,
pv5 = n0,
inference(resolve,[status(thm)],[c_401,c_1367]) ).
cnf(c_1368,negated_conjecture,
gt(n0,n0),
inference(paramod,[status(thm)],[c_1350,c_403]) ).
cnf(c_1365,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_1368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV193+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 13:22:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 4171368 was started by sandbox on n015,
% 0.10/0.36 % Sat Sep 26 13:22:13 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 2.45/0.77
% 2.45/0.77 % SZS status Theorem for theBenchmark
% 2.45/0.77
% 2.45/0.77 % Proof 1 at 0.29 (+ 0.06) seconds.
% 2.45/0.77 % Length of proof is 10.
% 2.45/0.77 % Level of proof is 3.
% 2.45/0.77 % Maximum clause weight is 11.000.
% 2.45/0.77 % Given clauses 311.
% 2.45/0.77
% 2.45/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------