%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV167+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 05:20:58 PM UTC 2026
% Result : Theorem 1.35s 1.73s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 205 ( 58 equ)
% Maximal formula atoms : 45 ( 6 avg)
% Number of connectives : 230 ( 55 ~; 53 |; 78 &)
% ( 2 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(cl5_nebula_init_0011,conjecture,
( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,n135299) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,n4) )
=> a_select3(q_init,X14,X18) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init )
& ! [X20] :
( ( leq(n0,X20)
& leq(X20,pred(pv40)) )
=> a_select2(mu_init,X20) = init )
& ! [X21] :
( ( leq(n0,X21)
& leq(X21,pred(pv40)) )
=> a_select2(sigma_init,X21) = init )
& ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select3(center_init,X22,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) )
& ( gt(loopcounter,n1)
=> ! [X29] :
( ( leq(n0,X29)
& leq(X29,n4) )
=> a_select2(rhoold_init,X29) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigmaold_init,X5) = init ) ) )
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,pv40) )
=> a_select2(mu_init,X11) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0011) ).
fof(leq_gt_pred,axiom,
! [X1,X2] :
( leq(X1,pred(X2))
<=> gt(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(leq_gt2,axiom,
! [X1,X2] :
( ( leq(X1,X2)
& X1 != X2 )
=> gt(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(c_0_4,plain,
( epred2_0
<=> ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,n135299) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,n4) )
=> a_select3(q_init,X14,X18) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init )
& ! [X20] :
( ( leq(n0,X20)
& leq(X20,pred(pv40)) )
=> a_select2(mu_init,X20) = init )
& ! [X21] :
( ( leq(n0,X21)
& leq(X21,pred(pv40)) )
=> a_select2(sigma_init,X21) = init )
& ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select3(center_init,X22,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) )
& ( gt(loopcounter,n1)
=> ! [X29] :
( ( leq(n0,X29)
& leq(X29,n4) )
=> a_select2(rhoold_init,X29) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigmaold_init,X5) = init ) ) ) ),
introduced(definition) ).
fof(c_0_5,plain,
( epred2_0
=> ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,n135299) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,n4) )
=> a_select3(q_init,X14,X18) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init )
& ! [X20] :
( ( leq(n0,X20)
& leq(X20,pred(pv40)) )
=> a_select2(mu_init,X20) = init )
& ! [X21] :
( ( leq(n0,X21)
& leq(X21,pred(pv40)) )
=> a_select2(sigma_init,X21) = init )
& ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select3(center_init,X22,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) )
& ( gt(loopcounter,n1)
=> ! [X29] :
( ( leq(n0,X29)
& leq(X29,n4) )
=> a_select2(rhoold_init,X29) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigmaold_init,X5) = init ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X381,X382,X383,X384,X385,X386,X387,X388,X389] :
( ( a_select2(mu_init,pv40) = init
| ~ epred2_0 )
& ( a_select2(sigma_init,pv40) = init
| ~ epred2_0 )
& ( leq(n0,pv40)
| ~ epred2_0 )
& ( leq(pv40,n4)
| ~ epred2_0 )
& ( ~ leq(n0,X381)
| ~ leq(X381,n135299)
| ~ leq(n0,X382)
| ~ leq(X382,n4)
| a_select3(q_init,X381,X382) = init
| ~ epred2_0 )
& ( ~ leq(n0,X383)
| ~ leq(X383,n4)
| a_select2(rho_init,X383) = init
| ~ epred2_0 )
& ( ~ leq(n0,X384)
| ~ leq(X384,pred(pv40))
| a_select2(mu_init,X384) = init
| ~ epred2_0 )
& ( ~ leq(n0,X385)
| ~ leq(X385,pred(pv40))
| a_select2(sigma_init,X385) = init
| ~ epred2_0 )
& ( ~ leq(n0,X386)
| ~ leq(X386,n4)
| a_select3(center_init,X386,n0) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n1)
| ~ leq(n0,X387)
| ~ leq(X387,n4)
| a_select2(muold_init,X387) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n1)
| ~ leq(n0,X388)
| ~ leq(X388,n4)
| a_select2(rhoold_init,X388) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n1)
| ~ leq(n0,X389)
| ~ leq(X389,n4)
| a_select2(sigmaold_init,X389) = init
| ~ epred2_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X325] : minus(X325,n1) = pred(X325),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_8,negated_conjecture,
~ ( epred2_0
=> ! [X11] :
( ( leq(n0,X11)
& leq(X11,pv40) )
=> a_select2(mu_init,X11) = init ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cl5_nebula_init_0011]),c_0_4]) ).
cnf(c_0_9,plain,
( a_select2(mu_init,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv40))
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( epred2_0
& leq(n0,esk24_0)
& leq(esk24_0,pv40)
& a_select2(mu_init,esk24_0) != init ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X226,X227] :
( ( ~ leq(X226,pred(X227))
| gt(X227,X226) )
& ( ~ gt(X227,X226)
| leq(X226,pred(X227)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt_pred])]) ).
cnf(c_0_13,plain,
( a_select2(mu_init,X1) = init
| ~ epred2_0
| ~ leq(n0,X1)
| ~ leq(X1,minus(pv40,n1)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( leq(X2,pred(X1))
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X224,X225] :
( ~ leq(X224,X225)
| X224 = X225
| gt(X225,X224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt2])]) ).
cnf(c_0_17,plain,
( a_select2(mu_init,X1) = init
| ~ leq(X1,minus(pv40,n1))
| ~ leq(n0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
cnf(c_0_18,plain,
( leq(X2,minus(X1,n1))
| ~ gt(X1,X2) ),
inference(rw,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_19,plain,
( X1 = X2
| gt(X2,X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
leq(esk24_0,pv40),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
a_select2(mu_init,esk24_0) != init,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( a_select2(mu_init,X1) = init
| ~ leq(n0,X1)
| ~ gt(pv40,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
leq(n0,esk24_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( esk24_0 = pv40
| gt(pv40,esk24_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ gt(pv40,esk24_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
( a_select2(mu_init,pv40) = init
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
esk24_0 = pv40,
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
a_select2(mu_init,pv40) = init,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_14])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV167+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n004.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:57:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.35/1.73 % Version : CSE_E---1.7
% 1.35/1.73 % Problem : theBenchmark.p
% 1.35/1.73 % SZS status Theorem for theBenchmark.p
% 1.35/1.73 % SZS output start CNFRefutation
% See solution above
% 1.35/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------