%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV202+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 : n028.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 05:21:04 PM UTC 2026
% Result : Theorem 114.73s 70.36s
% Output : CNFRefutation 115.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 18 unt; 0 def)
% Number of atoms : 345 ( 179 equ)
% Maximal formula atoms : 72 ( 6 avg)
% Number of connectives : 399 ( 107 ~; 104 |; 170 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_gt,axiom,
! [X1,X2,X3] :
( ( gt(X1,X2)
& gt(X2,X3) )
=> gt(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',transitivity_gt) ).
fof(leq_gt2,axiom,
! [X1,X2] :
( ( leq(X1,X2)
& X1 != X2 )
=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(quaternion_ds1_inuse_0013,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,n998)
& gt(pv5,n0)
& ! [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(u_defuse,X21,X22) = use ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0013) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(leq_gt_pred,axiom,
! [X1,X2] :
( leq(X1,pred(X2))
<=> gt(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(totality,axiom,
! [X1,X2] :
( gt(X1,X2)
| gt(X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',totality) ).
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_8,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,n998)
& gt(pv5,n0)
& ! [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_9,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,n998)
& gt(pv5,n0)
& ! [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_8]) ).
fof(c_0_10,plain,
! [X204,X205,X206] :
( ~ gt(X204,X205)
| ~ gt(X205,X206)
| gt(X204,X206) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_gt])]) ).
fof(c_0_11,plain,
! [X218,X219] :
( ~ leq(X218,X219)
| X218 = X219
| gt(X219,X218) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt2])]) ).
fof(c_0_12,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(u_defuse,X21,X22) = use ) ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0013]),c_0_8]) ).
fof(c_0_13,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,n998)
| ~ epred2_0 )
& ( gt(pv5,n0)
| ~ 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_9])])])]) ).
fof(c_0_14,plain,
! [X319] : minus(X319,n1) = pred(X319),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_15,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
cnf(c_0_16,plain,
( gt(X1,X3)
| ~ gt(X1,X2)
| ~ gt(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( X1 = X2
| gt(X2,X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,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(u_defuse,esk24_0,esk25_0) != use ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_19,plain,
( a_select3(u_defuse,X1,X2) = use
| ~ leq(n0,X1)
| ~ leq(n0,X2)
| ~ leq(X1,n2)
| ~ leq(X2,pred(pv5))
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X220,X221] :
( ( ~ leq(X220,pred(X221))
| gt(X221,X220) )
& ( ~ gt(X221,X220)
| leq(X220,pred(X221)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt_pred])]) ).
fof(c_0_22,plain,
! [X207] : ~ gt(X207,X207),
inference(variable_rename,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( X1 = X2
| gt(X3,X1)
| ~ leq(X1,X2)
| ~ gt(X3,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
leq(esk25_0,pv5),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( a_select3(u_defuse,X1,X2) = use
| ~ epred2_0
| ~ leq(X1,n2)
| ~ leq(n0,X2)
| ~ leq(n0,X1)
| ~ leq(X2,minus(pv5,n1)) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( leq(X2,pred(X1))
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( esk25_0 = pv5
| gt(X1,esk25_0)
| ~ gt(X1,pv5) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_30,plain,
! [X202,X203] :
( gt(X202,X203)
| gt(X203,X202)
| X202 = X203 ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_31,plain,
( a_select3(u_defuse,X1,X2) = use
| ~ leq(X2,minus(pv5,n1))
| ~ leq(X1,n2)
| ~ leq(n0,X2)
| ~ leq(n0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_32,plain,
( leq(X2,minus(X1,n1))
| ~ gt(X1,X2) ),
inference(rw,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_33,negated_conjecture,
( esk25_0 = pv5
| ~ gt(esk25_0,pv5) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( gt(X1,X2)
| gt(X2,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( a_select3(u_defuse,X1,X2) = use
| ~ leq(X1,n2)
| ~ leq(n0,X2)
| ~ leq(n0,X1)
| ~ gt(pv5,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( esk25_0 = pv5
| gt(pv5,esk25_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
leq(n0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_38,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_39,negated_conjecture,
a_select3(u_defuse,esk24_0,esk25_0) != use,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_40,plain,
( a_select3(u_defuse,X1,esk25_0) = use
| esk25_0 = pv5
| ~ leq(X1,n2)
| ~ leq(n0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_41,negated_conjecture,
leq(esk24_0,n2),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,negated_conjecture,
leq(n0,esk24_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,plain,
( X1 = n0
| X1 = n1
| X1 = n2
| ~ leq(n0,X1)
| ~ leq(X1,n2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( n2 != esk24_0
| pv5 != esk25_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_45,negated_conjecture,
esk25_0 = pv5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
( n0 != esk24_0
| pv5 != esk25_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_47,negated_conjecture,
( n1 != esk24_0
| pv5 != esk25_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_48,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_43,c_0_41]),c_0_42])]) ).
cnf(c_0_49,negated_conjecture,
esk24_0 != n2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_50,negated_conjecture,
esk24_0 != n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_45])]) ).
cnf(c_0_51,negated_conjecture,
esk24_0 != n1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_45])]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV202+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 : n028.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 04:58:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 114.73/70.36 % Version : CSE_E---1.7
% 114.73/70.36 % Problem : theBenchmark.p
% 114.73/70.36 % SZS status Theorem for theBenchmark.p
% 114.73/70.36 % SZS output start CNFRefutation
% See solution above
% 115.23/70.80 % Total time : 53.126s
%------------------------------------------------------------------------------