%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV199+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:21:03 PM UTC 2026
% Result : Theorem 1.85s 1.89s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 286 ( 169 equ)
% Maximal formula atoms : 72 ( 8 avg)
% Number of connectives : 329 ( 78 ~; 67 |; 168 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 18 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_inuse_0010,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
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n2)
& leq(X18,pred(pv5)) )
=> a_select3(u_defuse,X14,X18) = use )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,pred(pv5)) )
=> a_select3(z_defuse,X4,X20) = use ) )
=> ! [X21,X22] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n2)
& leq(X22,pv5) )
=> ( ( ~ ( n0 = X21
& pv5 = X22 )
& ~ ( n1 = X21
& pv5 = X22 )
& ~ ( n2 = X21
& pv5 = X22 ) )
=> a_select3(z_defuse,X21,X22) = use ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0010) ).
fof(finite_domain_0,axiom,
! [X1] :
( ( leq(n0,X1)
& leq(X1,n0) )
=> X1 = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
fof(finite_domain_2,axiom,
! [X1] :
( ( leq(n0,X1)
& leq(X1,n2) )
=> ( X1 = n0
| X1 = n1
| X1 = n2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
fof(c_0_3,plain,
( epred2_0
<=> ( 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
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n2)
& leq(X18,pred(pv5)) )
=> a_select3(u_defuse,X14,X18) = use )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,pred(pv5)) )
=> a_select3(z_defuse,X4,X20) = use ) ) ),
introduced(definition) ).
fof(c_0_4,plain,
( epred2_0
=> ( 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
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n2)
& leq(X18,pred(pv5)) )
=> a_select3(u_defuse,X14,X18) = use )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,pred(pv5)) )
=> a_select3(z_defuse,X4,X20) = use ) ) ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
fof(c_0_5,negated_conjecture,
~ ( epred2_0
=> ! [X21,X22] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n2)
& leq(X22,pv5) )
=> ( ( ~ ( n0 = X21
& pv5 = X22 )
& ~ ( n1 = X21
& pv5 = X22 )
& ~ ( n2 = X21
& pv5 = X22 ) )
=> a_select3(z_defuse,X21,X22) = use ) ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0010]),c_0_3]) ).
fof(c_0_6,plain,
! [X376,X377,X378,X379] :
( ( a_select2(rho_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(rho_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(rho_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n5) = use
| ~ epred2_0 )
& ( a_select3(u_defuse,n0,n0) = use
| ~ epred2_0 )
& ( a_select3(u_defuse,n1,n0) = use
| ~ epred2_0 )
& ( a_select3(u_defuse,n2,n0) = use
| ~ epred2_0 )
& ( a_select2(xinit_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(xinit_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(xinit_defuse,n5) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n5) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n5) = use
| ~ epred2_0 )
& ( leq(n0,pv5)
| ~ epred2_0 )
& ( leq(pv5,n0)
| ~ epred2_0 )
& ( leq(pv5,n998)
| ~ epred2_0 )
& ( ~ leq(n0,X376)
| ~ leq(n0,X377)
| ~ leq(X376,n2)
| ~ leq(X377,pred(pv5))
| a_select3(u_defuse,X376,X377) = use
| ~ epred2_0 )
& ( ~ leq(n0,X378)
| ~ leq(n0,X379)
| ~ leq(X378,n2)
| ~ leq(X379,pred(pv5))
| a_select3(z_defuse,X378,X379) = use
| ~ epred2_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,negated_conjecture,
( epred2_0
& leq(n0,esk24_0)
& leq(n0,esk25_0)
& leq(esk24_0,n2)
& leq(esk25_0,pv5)
& ( n0 != esk24_0
| pv5 != esk25_0 )
& ( n1 != esk24_0
| pv5 != esk25_0 )
& ( n2 != esk24_0
| pv5 != esk25_0 )
& a_select3(z_defuse,esk24_0,esk25_0) != use ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X364] :
( ~ leq(n0,X364)
| ~ leq(X364,n0)
| X364 = n0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[finite_domain_0])]) ).
cnf(c_0_9,plain,
( leq(pv5,n0)
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( leq(n0,pv5)
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( X1 = n0
| ~ leq(n0,X1)
| ~ leq(X1,n0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
leq(pv5,n0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).
cnf(c_0_14,plain,
leq(n0,pv5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10])]) ).
cnf(c_0_15,negated_conjecture,
leq(esk25_0,pv5),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
pv5 = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
fof(c_0_17,plain,
! [X366] :
( ~ leq(n0,X366)
| ~ leq(X366,n2)
| X366 = n0
| X366 = n1
| X366 = n2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[finite_domain_2])]) ).
cnf(c_0_18,negated_conjecture,
( n0 != esk24_0
| pv5 != esk25_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
leq(esk25_0,n0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
leq(n0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
( n1 != esk24_0
| pv5 != esk25_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,plain,
( X1 = n0
| X1 = n1
| X1 = n2
| ~ leq(n0,X1)
| ~ leq(X1,n2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
leq(esk24_0,n2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
leq(n0,esk24_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( esk24_0 != n0
| esk25_0 != n0 ),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
esk25_0 = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_19]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
( esk24_0 != n1
| esk25_0 != n0 ),
inference(rw,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
( n2 != esk24_0
| pv5 != esk25_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,negated_conjecture,
( esk24_0 = n0
| esk24_0 = n1
| esk24_0 = n2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,negated_conjecture,
esk24_0 != n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
esk24_0 != n1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_26])]) ).
cnf(c_0_32,negated_conjecture,
( esk24_0 != n2
| esk25_0 != n0 ),
inference(rw,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_33,negated_conjecture,
esk24_0 = n2,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_26])]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV199+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:58:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.85/1.89 % Version : CSE_E---1.7
% 1.85/1.89 % Problem : theBenchmark.p
% 1.85/1.89 % SZS status Theorem for theBenchmark.p
% 1.85/1.89 % SZS output start CNFRefutation
% See solution above
% 1.85/1.89 % Total time : 1.370s
%------------------------------------------------------------------------------