%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV181+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 : 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 05:21:01 PM UTC 2026
% Result : Theorem 1.37s 1.74s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 19 unt; 0 def)
% Number of atoms : 181 ( 40 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 185 ( 49 ~; 46 |; 53 &)
% ( 2 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 15 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0081,conjecture,
( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X4,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n4) )
=> a_select2(mu_init,X20) = init ) )
& ( gt(loopcounter,n0)
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n4) )
=> a_select2(rho_init,X21) = init ) )
& ( gt(loopcounter,n0)
=> ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select2(sigma_init,X22) = init ) ) )
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0081) ).
fof(leq_succ_gt,axiom,
! [X1,X2] :
( leq(succ(X1),X2)
=> gt(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ_gt) ).
fof(succ_plus_1_r,axiom,
! [X1] : plus(X1,n1) = succ(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(leq_gt1,axiom,
! [X1,X2] :
( gt(X2,X1)
=> leq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
fof(finite_domain_1,axiom,
! [X1] :
( ( leq(n0,X1)
& leq(X1,n1) )
=> ( X1 = n0
| X1 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(leq_succ_gt_equiv,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> gt(succ(X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
fof(c_0_8,plain,
( epred2_0
<=> ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X4,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n4) )
=> a_select2(mu_init,X20) = init ) )
& ( gt(loopcounter,n0)
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n4) )
=> a_select2(rho_init,X21) = init ) )
& ( gt(loopcounter,n0)
=> ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select2(sigma_init,X22) = init ) ) ) ),
introduced(definition) ).
fof(c_0_9,plain,
( epred2_0
=> ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X4,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n4) )
=> a_select2(mu_init,X20) = init ) )
& ( gt(loopcounter,n0)
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n4) )
=> a_select2(rho_init,X21) = init ) )
& ( gt(loopcounter,n0)
=> ! [X22] :
( ( leq(n0,X22)
& leq(X22,n4) )
=> a_select2(sigma_init,X22) = init ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_8]) ).
fof(c_0_10,negated_conjecture,
~ ( epred2_0
=> ! [X28] :
( ( leq(n0,X28)
& leq(X28,n4) )
=> a_select2(muold_init,X28) = init ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cl5_nebula_init_0081]),c_0_8]) ).
fof(c_0_11,plain,
! [X326,X327] :
( ~ leq(succ(X326),X327)
| gt(X327,X326) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt])]) ).
fof(c_0_12,plain,
! [X311] : plus(X311,n1) = succ(X311),
inference(variable_rename,[status(thm)],[succ_plus_1_r]) ).
fof(c_0_13,plain,
! [X377,X378,X379,X380,X381,X382] :
( ( leq(tptp_float_0_001,pv76)
| ~ epred2_0 )
& ( leq(n1,loopcounter)
| ~ epred2_0 )
& ( gt(n1,loopcounter)
| ~ epred2_0 )
& ( ~ leq(n0,X377)
| ~ leq(X377,n135299)
| ~ leq(n0,X378)
| ~ leq(X378,n4)
| a_select3(q_init,X377,X378) = init
| ~ epred2_0 )
& ( ~ leq(n0,X379)
| ~ leq(X379,n4)
| a_select3(center_init,X379,n0) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n0)
| ~ leq(n0,X380)
| ~ leq(X380,n4)
| a_select2(mu_init,X380) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n0)
| ~ leq(n0,X381)
| ~ leq(X381,n4)
| a_select2(rho_init,X381) = init
| ~ epred2_0 )
& ( ~ gt(loopcounter,n0)
| ~ leq(n0,X382)
| ~ leq(X382,n4)
| a_select2(sigma_init,X382) = init
| ~ 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,negated_conjecture,
( epred2_0
& leq(n0,esk24_0)
& leq(esk24_0,n4)
& a_select2(muold_init,esk24_0) != init ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,plain,
( gt(X2,X1)
| ~ leq(succ(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
fof(c_0_18,plain,
! [X218,X219] :
( ~ gt(X219,X218)
| leq(X218,X219) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt1])]) ).
cnf(c_0_19,plain,
( gt(n1,loopcounter)
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( gt(X2,X1)
| ~ leq(plus(X1,n1),X2) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
fof(c_0_23,plain,
! [X366] :
( ~ leq(n0,X366)
| ~ leq(X366,n1)
| X366 = n0
| X366 = n1 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[finite_domain_1])]) ).
cnf(c_0_24,plain,
( leq(X2,X1)
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
gt(n1,loopcounter),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_26,plain,
( gt(X1,n0)
| ~ leq(n1,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( leq(n1,loopcounter)
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_28,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_29,plain,
! [X227,X228] :
( ( ~ leq(X227,X228)
| gt(succ(X228),X227) )
& ( ~ gt(succ(X228),X227)
| leq(X227,X228) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])]) ).
cnf(c_0_30,plain,
( X1 = n0
| X1 = n1
| ~ leq(n0,X1)
| ~ leq(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
leq(loopcounter,n1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( leq(n0,X1)
| ~ leq(n1,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_33,plain,
leq(n1,loopcounter),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_20])]) ).
fof(c_0_34,plain,
! [X209] : ~ gt(X209,X209),
inference(variable_rename,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( gt(succ(X2),X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( loopcounter = n1
| loopcounter = n0
| ~ leq(n0,loopcounter) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
leq(n0,loopcounter),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( gt(plus(X2,n1),X1)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[c_0_35,c_0_16]) ).
cnf(c_0_40,plain,
( loopcounter = n0
| loopcounter = n1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_41,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
loopcounter = n0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_40]),c_0_38]) ).
cnf(c_0_43,plain,
~ leq(n1,n0),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_44,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV181+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % 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 04:57:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.37/1.74 % Version : CSE_E---1.7
% 1.37/1.74 % Problem : theBenchmark.p
% 1.37/1.74 % SZS status Theorem for theBenchmark.p
% 1.37/1.74 % SZS output start CNFRefutation
% See solution above
% 1.37/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------