%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV153+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 : Thu Sep 24 02:53:50 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 102 ( 37 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 99 ( 26 ~; 15 |; 40 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0003,conjecture,
( ( ! [X18] :
( ( leq(X18,pred(pv10))
& leq(n0,X18) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 )
& ! [X14] :
( ( leq(X14,pred(pv12))
& leq(n0,X14) )
=> a_select3(q,pv10,X14) = divide(sqrt(times(minus(a_select3(center,X14,n0),a_select2(x,pv10)),minus(a_select3(center,X14,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [X4] :
( ( leq(X4,pv12)
& leq(n0,X4) )
=> ( pv12 != X4
=> a_select3(q,pv10,X4) = divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0003) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(leq_gt2,axiom,
! [X1,X2] :
( ( X1 != X2
& leq(X1,X2) )
=> gt(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(succ_pred,axiom,
! [X1] : succ(pred(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_pred) ).
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_5,negated_conjecture,
~ ( ( ! [X18] :
( ( leq(X18,pred(pv10))
& leq(n0,X18) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 )
& ! [X14] :
( ( leq(X14,pred(pv12))
& leq(n0,X14) )
=> a_select3(q,pv10,X14) = divide(sqrt(times(minus(a_select3(center,X14,n0),a_select2(x,pv10)),minus(a_select3(center,X14,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [X4] :
( ( leq(X4,pv12)
& leq(n0,X4) )
=> ( pv12 != X4
=> a_select3(q,pv10,X4) = divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0003]) ).
fof(c_0_6,negated_conjecture,
~ ( ( ! [X18] :
( ( leq(X18,pred(pv10))
& leq(n0,X18) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 )
& ! [X14] :
( ( leq(X14,pred(pv12))
& leq(n0,X14) )
=> a_select3(q,pv10,X14) = divide(sqrt(times(minus(a_select3(center,X14,n0),a_select2(x,pv10)),minus(a_select3(center,X14,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [X4] :
( ( leq(X4,pv12)
& leq(n0,X4) )
=> ( pv12 != X4
=> a_select3(q,pv10,X4) = divide(sqrt(times(minus(a_select3(center,X4,n0),a_select2(x,pv10)),minus(a_select3(center,X4,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X28,X29] :
( a_select3(q,pv10,esk1_0) != divide(sqrt(times(minus(a_select3(center,esk1_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk1_0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 != esk1_0
& leq(esk1_0,pv12)
& leq(n0,esk1_0)
& ( sum(n0,n4,a_select3(q,X29,tptp_sum_index)) = n1
| ~ leq(X29,pred(pv10))
| ~ leq(n0,X29) )
& ( a_select3(q,pv10,X28) = divide(sqrt(times(minus(a_select3(center,X28,n0),a_select2(x,pv10)),minus(a_select3(center,X28,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| ~ leq(X28,pred(pv12))
| ~ leq(n0,X28) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_8,plain,
! [X32] : minus(X32,n1) = pred(X32),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_9,plain,
! [X1,X2] :
( ( X1 != X2
& leq(X1,X2) )
=> gt(X2,X1) ),
inference(fof_simplification,[status(thm)],[leq_gt2]) ).
cnf(c_0_10,negated_conjecture,
a_select3(q,pv10,esk1_0) != divide(sqrt(times(minus(a_select3(center,esk1_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk1_0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( ~ leq(X1,pred(pv12))
| ~ leq(n0,X1)
| a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X62] : succ(pred(X62)) = X62,
inference(variable_rename,[status(thm)],[succ_pred]) ).
fof(c_0_15,plain,
! [X46,X47] :
( gt(X47,X46)
| X46 = X47
| ~ leq(X46,X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_16,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,esk1_0,n0),a_select2(x,pv10)),minus(a_select3(center,esk1_0,n0),a_select2(x,pv10)))),pv70) != a_select3(q,pv10,esk1_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( ~ leq(n0,X1)
| ~ leq(X1,minus(pv12,n1))
| divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),pv70) = a_select3(q,pv10,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_13]) ).
cnf(c_0_18,negated_conjecture,
leq(n0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_19,plain,
! [X50,X51] :
( ( leq(X50,X51)
| ~ gt(succ(X51),X50) )
& ( gt(succ(X51),X50)
| ~ leq(X50,X51) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])])]) ).
cnf(c_0_20,plain,
succ(pred(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ leq(X1,X2)
| gt(X2,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
leq(esk1_0,pv12),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
pv12 != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
~ leq(esk1_0,minus(pv12,n1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_25,plain,
( ~ gt(succ(X1),X2)
| leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
succ(minus(X1,n1)) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_27,negated_conjecture,
gt(pv12,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV153+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:38:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % new_bool_3 with pid 2034785 completed with status 0
% 0.14/0.45 % Result found by new_bool_3
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.45 % Search class: FGUSM-FFMM31-DFFFFFNN
% 0.14/0.45 % partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.14/0.45 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.45 % SubtermCWHack with pid 2034789 completed with status 0
% 0.14/0.45 % Result found by SubtermCWHack
% 0.14/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.45 % Search class: FGUSM-FFMM31-DFFFFFNN
% 0.14/0.45 % partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.14/0.45 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.45 % Preprocessing time : 0.002 s
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 92
% 0.14/0.45 % Removed by relevancy pruning/SinE : 23
% 0.14/0.45 % Initial clauses : 82
% 0.14/0.45 % Removed in clause preprocessing : 0
% 0.14/0.45 % Initial clauses in saturation : 82
% 0.14/0.45 % Processed clauses : 355
% 0.14/0.45 % ...of these trivial : 1
% 0.14/0.45 % ...subsumed : 121
% 0.14/0.45 % ...remaining for further processing : 233
% 0.14/0.45 % Other redundant clauses eliminated : 0
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 1
% 0.14/0.45 % Backward-rewritten : 10
% 0.14/0.45 % Generated clauses : 854
% 0.14/0.45 % ...of the previous two non-redundant : 570
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 0
% 0.14/0.45 % Paramodulations : 852
% 0.14/0.45 % Factorizations : 2
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 0
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 397
% 0.14/0.45 % ...of those cached : 327
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 222
% 0.14/0.45 % Positive orientable unit clauses : 98
% 0.14/0.45 % Positive unorientable unit clauses: 0
% 0.14/0.45 % Negative unit clauses : 32
% 0.14/0.45 % Non-unit-clauses : 92
% 0.14/0.45 % Current number of unprocessed clauses: 296
% 0.14/0.45 % ...number of literals in the above : 769
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 11
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 2500
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 2299
% 0.14/0.45 % Non-unit clause-clause subsumptions : 27
% 0.14/0.45 % Unit Clause-clause subsumption calls : 621
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 13
% 0.14/0.45 % BW rewrite match successes : 6
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 11399
% 0.14/0.45 % Search garbage collected termcells : 754
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.015 s
% 0.14/0.45 % System time : 0.005 s
% 0.14/0.45 % Total time : 0.020 s
% 0.14/0.45 % Maximum resident set size: 3748 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.018 s
% 0.14/0.45 % System time : 0.010 s
% 0.14/0.45 % Total time : 0.028 s
% 0.14/0.45 % Maximum resident set size: 4608 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------