%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV050+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 : n013.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 02:53:35 PM UTC 2026
% Result : Theorem 0.24s 0.47s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 34 unt; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 21 ( 7 ~; 4 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-3 aty)
% Number of variables : 10 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(successor_2,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
fof(pred_succ,axiom,
! [X1] : pred(succ(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
fof(cl5_nebula_norm_0022,conjecture,
( ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
=> ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0022) ).
fof(successor_5,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_tptp_minus_1) ).
fof(sum_plus_base,axiom,
! [X23] : sum(n0,tptp_minus_1,X23) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sum_plus_base) ).
cnf(c_0_10,plain,
succ(succ(n0)) = n2,
inference(split_conjunct,[status(thm)],[successor_2]) ).
cnf(c_0_11,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[successor_1]) ).
cnf(c_0_12,plain,
succ(succ(succ(n0))) = n3,
inference(split_conjunct,[status(thm)],[successor_3]) ).
cnf(c_0_13,plain,
succ(n1) = n2,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_14,plain,
! [X59] : pred(succ(X59)) = X59,
inference(variable_rename,[status(thm)],[pred_succ]) ).
fof(c_0_15,plain,
! [X39] : minus(X39,n1) = pred(X39),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
cnf(c_0_16,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(split_conjunct,[status(thm)],[successor_4]) ).
cnf(c_0_17,plain,
succ(n2) = n3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_13]) ).
fof(c_0_18,negated_conjecture,
~ ( ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
=> ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0022]) ).
cnf(c_0_19,plain,
pred(succ(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(split_conjunct,[status(thm)],[successor_5]) ).
cnf(c_0_22,plain,
succ(n3) = n4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_11]),c_0_13]),c_0_17]) ).
cnf(c_0_23,plain,
succ(tptp_minus_1) = n0,
inference(split_conjunct,[status(thm)],[succ_tptp_minus_1]) ).
fof(c_0_24,negated_conjecture,
( ( pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_25,plain,
minus(succ(X1),n1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
succ(n4) = n5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_11]),c_0_13]),c_0_17]),c_0_22]) ).
cnf(c_0_27,plain,
pred(n0) = tptp_minus_1,
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
fof(c_0_28,plain,
! [X28] : sum(n0,tptp_minus_1,X28) = n0,
inference(variable_rename,[status(thm)],[sum_plus_base]) ).
cnf(c_0_29,negated_conjecture,
pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
minus(n5,n1) = n4,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
minus(n0,n1) = tptp_minus_1,
inference(rw,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_34,plain,
sum(n0,tptp_minus_1,X1) = n0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
sum(n0,n4,divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) = pv86,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
sum(n0,n4,divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) = pv88,
inference(rw,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_30]),c_0_35]),c_0_30]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV050+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 : n013.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 08:28:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.24/0.47 % Version: 3.5.1
% 0.24/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.24/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.24/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.47 % Starting sh5l with 300s (1) cores
% 0.24/0.47 % new_bool_3 with pid 362921 completed with status 0
% 0.24/0.47 % Result found by new_bool_3
% 0.24/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.24/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.24/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.47 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.24/0.47 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.47 % SubtermCWHack with pid 362924 completed with status 0
% 0.24/0.47 % Result found by SubtermCWHack
% 0.24/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.24/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.24/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.47 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.24/0.47 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.47 % Preprocessing time : 0.002 s
% 0.24/0.47
% 0.24/0.47 % Proof found!
% 0.24/0.47 % SZS status Theorem
% 0.24/0.47 % SZS output start CNFRefutation
% See solution above
% 0.24/0.47 % Parsed axioms : 85
% 0.24/0.47 % Removed by relevancy pruning/SinE : 23
% 0.24/0.47 % Initial clauses : 67
% 0.24/0.47 % Removed in clause preprocessing : 0
% 0.24/0.47 % Initial clauses in saturation : 67
% 0.24/0.47 % Processed clauses : 319
% 0.24/0.47 % ...of these trivial : 0
% 0.24/0.47 % ...subsumed : 129
% 0.24/0.47 % ...remaining for further processing : 189
% 0.24/0.47 % Other redundant clauses eliminated : 0
% 0.24/0.47 % Clauses deleted for lack of memory : 0
% 0.24/0.47 % Backward-subsumed : 1
% 0.24/0.47 % Backward-rewritten : 10
% 0.24/0.47 % Generated clauses : 799
% 0.24/0.47 % ...of the previous two non-redundant : 478
% 0.24/0.47 % ...aggressively subsumed : 0
% 0.24/0.47 % Contextual simplify-reflections : 0
% 0.24/0.47 % Paramodulations : 797
% 0.24/0.47 % Factorizations : 2
% 0.24/0.47 % NegExts : 0
% 0.24/0.47 % Equation resolutions : 0
% 0.24/0.47 % Disequality decompositions : 0
% 0.24/0.47 % Total rewrite steps : 434
% 0.24/0.47 % ...of those cached : 383
% 0.24/0.47 % Propositional unsat checks : 0
% 0.24/0.47 % Propositional check models : 0
% 0.24/0.47 % Propositional check unsatisfiable : 0
% 0.24/0.47 % Propositional clauses : 0
% 0.24/0.47 % Propositional clauses after purity: 0
% 0.24/0.47 % Propositional unsat core size : 0
% 0.24/0.47 % Propositional preprocessing time : 0.000
% 0.24/0.47 % Propositional encoding time : 0.000
% 0.24/0.47 % Propositional solver time : 0.000
% 0.24/0.47 % Success case prop preproc time : 0.000
% 0.24/0.47 % Success case prop encoding time : 0.000
% 0.24/0.47 % Success case prop solver time : 0.000
% 0.24/0.47 % Current number of processed clauses : 178
% 0.24/0.47 % Positive orientable unit clauses : 65
% 0.24/0.47 % Positive unorientable unit clauses: 0
% 0.24/0.47 % Negative unit clauses : 28
% 0.24/0.47 % Non-unit-clauses : 85
% 0.24/0.47 % Current number of unprocessed clauses: 226
% 0.24/0.47 % ...number of literals in the above : 604
% 0.24/0.47 % Current number of archived formulas : 0
% 0.24/0.47 % Current number of archived clauses : 11
% 0.24/0.47 % Clause-clause subsumption calls (NU) : 1377
% 0.24/0.47 % Rec. Clause-clause subsumption calls : 1082
% 0.24/0.47 % Non-unit clause-clause subsumptions : 26
% 0.24/0.47 % Unit Clause-clause subsumption calls : 338
% 0.24/0.47 % Rewrite failures with RHS unbound : 0
% 0.24/0.47 % BW rewrite match attempts : 7
% 0.24/0.47 % BW rewrite match successes : 6
% 0.24/0.47 % Condensation attempts : 0
% 0.24/0.47 % Condensation successes : 0
% 0.24/0.47 % Termbank termtop insertions : 10147
% 0.24/0.47 % Search garbage collected termcells : 582
% 0.24/0.47
% 0.24/0.47 % -------------------------------------------------
% 0.24/0.47 % User time : 0.015 s
% 0.24/0.47 % System time : 0.003 s
% 0.24/0.47 % Total time : 0.018 s
% 0.24/0.47 % Maximum resident set size: 3740 pages
% 0.24/0.47
% 0.24/0.47 % -------------------------------------------------
% 0.24/0.47 % User time : 0.018 s
% 0.24/0.47 % System time : 0.009 s
% 0.24/0.47 % Total time : 0.026 s
% 0.24/0.47 % Maximum resident set size: 4608 pages
% 0.24/0.47 % E exiting
%------------------------------------------------------------------------------