%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 03:48:17 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 58 ( 15 unt; 0 nHn; 25 RR)
% Number of literals : 276 ( 0 equ; 230 neg)
% Maximal clause size : 11 ( 4 avg)
% Maximal term depth : 14 ( 4 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 263 ( 251 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_21_01,axiom,
( ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s(s(s('0'))))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21_01) ).
cnf(clause_12_14,axiom,
( ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s(s('0')))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_14) ).
cnf(clause_17_09,axiom,
'E'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17_09) ).
cnf(clause_11_03,axiom,
'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0'))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_03) ).
cnf(clause_1_06,axiom,
( ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s('0'))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_06) ).
cnf(clause_15_20,axiom,
( ~ 'E'(f(X5),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f(X2),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15_20) ).
cnf(clause_3_17,axiom,
( ~ 'E'(f(X11),'0')
| ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X8),s(s(s('0'))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X6),s(s('0')))
| ~ 'E'(f(X5),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_17) ).
cnf(clause_9_12,axiom,
( ~ 'E'(f(X6),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_12) ).
cnf(clause_18_15,axiom,
( ~ 'E'(f(X7),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X6),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_15) ).
cnf(clause_0_19,axiom,
( ~ 'E'(f(X8),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X6),s(s(s('0'))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_19) ).
cnf(clause_8_11,axiom,
( ~ 'E'(f(X9),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X7),s(s(s('0'))))
| ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X5),s(s('0')))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_11) ).
cnf(clause_10_22,axiom,
( ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X8),s(s(s('0'))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X6),s(s('0')))
| ~ 'E'(f(X5),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X11)),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_22) ).
cnf(c_0_12,plain,
( ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(fof_simplification,[status(thm)],[clause_21_01]) ).
cnf(c_0_13,plain,
( ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s(s('0')))))))) ),
inference(fof_simplification,[status(thm)],[clause_12_14]) ).
cnf(c_0_14,plain,
( ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s(s(s('0'))))))))) ),
c_0_12 ).
cnf(c_0_15,axiom,
'E'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))),
clause_17_09 ).
cnf(c_0_16,axiom,
'E'(f(X1),s(s(s(s(s(s(s(s(s(s('0'))))))))))),
clause_11_03 ).
cnf(c_0_17,plain,
( ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s('0'))))))) ),
inference(fof_simplification,[status(thm)],[clause_1_06]) ).
cnf(c_0_18,plain,
( ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s(s('0')))))))) ),
c_0_13 ).
cnf(c_0_19,plain,
'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,plain,
( ~ 'E'(f(X5),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f(X2),s(s(s(s(s('0')))))) ),
inference(fof_simplification,[status(thm)],[clause_15_20]) ).
cnf(c_0_21,plain,
( ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s('0')))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(f(X2),s(s(s(s(s(s('0'))))))) ),
c_0_17 ).
cnf(c_0_22,plain,
'E'(f(X1),s(s(s(s(s(s(s('0')))))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_23,plain,
( ~ 'E'(f(X11),'0')
| ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X8),s(s(s('0'))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X6),s(s('0')))
| ~ 'E'(f(X5),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(fof_simplification,[status(thm)],[clause_3_17]) ).
cnf(c_0_24,plain,
( ~ 'E'(f(X5),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X2),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f(X2),s(s(s(s(s('0')))))) ),
c_0_20 ).
cnf(c_0_25,plain,
'E'(f(X1),s(s(s(s(s(s('0'))))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_26,plain,
( ~ 'E'(f(X6),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s(s('0'))))) ),
inference(fof_simplification,[status(thm)],[clause_9_12]) ).
cnf(c_0_27,plain,
( ~ 'E'(f(X7),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X6),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s(s('0')))) ),
inference(fof_simplification,[status(thm)],[clause_18_15]) ).
cnf(c_0_28,plain,
( ~ 'E'(f(X8),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X6),s(s(s('0'))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s(s('0'))) ),
inference(fof_simplification,[status(thm)],[clause_0_19]) ).
cnf(c_0_29,plain,
( ~ 'E'(f(X9),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X7),s(s(s('0'))))
| ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X5),s(s('0')))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),s('0')) ),
inference(fof_simplification,[status(thm)],[clause_8_11]) ).
cnf(c_0_30,plain,
( ~ 'E'(f(X11),'0')
| ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X8),s(s(s('0'))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X6),s(s('0')))
| ~ 'E'(f(X5),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) ),
c_0_23 ).
cnf(c_0_31,plain,
'E'(f(X1),s(s(s(s(s('0')))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_32,plain,
( ~ 'E'(f(X6),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X7)),s(s(s(s('0'))))) ),
c_0_26 ).
cnf(c_0_33,plain,
( ~ 'E'(f(X7),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X6),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X8)),s(s(s('0')))) ),
c_0_27 ).
cnf(c_0_34,plain,
( ~ 'E'(f(X8),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X6),s(s(s('0'))))
| ~ 'E'(f(X5),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X9)),s(s('0'))) ),
c_0_28 ).
cnf(c_0_35,plain,
( ~ 'E'(f(X9),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X8),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X7),s(s(s('0'))))
| ~ 'E'(f(X6),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X5),s(s('0')))
| ~ 'E'(f(X4),s(s(s(s('0')))))
| ~ 'E'(f(X3),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X10)),s('0')) ),
c_0_29 ).
cnf(c_0_36,plain,
( ~ 'E'(f(X5),'0')
| ~ 'E'(f(X4),s('0'))
| ~ 'E'(f(X3),s(s('0')))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s('0'))))) ),
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_30,c_0_31]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_37,plain,
'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s(s(s('0'))))),
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_31]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_38,plain,
( ~ 'E'(f(X2),s(s(s(s('0')))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s(s('0')))) ),
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_33,c_0_31]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_39,plain,
( ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X2),s(s(s(s('0')))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s('0'))) ),
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_34,c_0_31]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_40,plain,
( ~ 'E'(f(X4),s(s('0')))
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X2),s(s(s(s('0')))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s('0')) ),
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_35,c_0_31]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_41,plain,
( ~ 'E'(f(X4),'0')
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s('0')))
| ~ 'E'(f(X1),s(s(s('0')))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s(s('0')))),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_43,plain,
( ~ 'E'(f(X2),s(s(s('0'))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s('0'))) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_44,plain,
( ~ 'E'(f(X3),s(s('0')))
| ~ 'E'(f(X2),s(s(s('0'))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s('0')) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_45,plain,
( ~ 'E'(f(X3),'0')
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X1),s(s('0'))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s(s('0'))),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_47,plain,
( ~ 'E'(f(X2),s(s('0')))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s('0')) ),
inference(spm,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_48,plain,
( ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X8),s(s(s('0'))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X6),s(s('0')))
| ~ 'E'(f(X5),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X11)),'0') ),
inference(fof_simplification,[status(thm)],[clause_10_22]) ).
cnf(c_0_49,plain,
( ~ 'E'(f(X2),'0')
| ~ 'E'(f(X1),s('0')) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X1)),s('0')),
inference(spm,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_51,plain,
( ~ 'E'(f(X10),s(s(s(s(s(s('0')))))))
| ~ 'E'(f(X9),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ 'E'(f(X8),s(s(s('0'))))
| ~ 'E'(f(X7),s(s(s(s(s(s(s('0'))))))))
| ~ 'E'(f(X6),s(s('0')))
| ~ 'E'(f(X5),s(s(s(s('0')))))
| ~ 'E'(f(X4),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(f('AP'(s(s(s(s(s(s(s(s(s(s(s('0'))))))))))),X11)),'0') ),
c_0_48 ).
cnf(c_0_52,plain,
~ 'E'(f(X1),'0'),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
( ~ 'E'(f(X4),s('0'))
| ~ 'E'(f(X3),s(s('0')))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s('0'))))) ),
inference(sr,[status(thm)],[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_51,c_0_31]),c_0_25]),c_0_22]),c_0_19]),c_0_15]),c_0_16])]),c_0_52]) ).
cnf(c_0_54,plain,
( ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s('0')))
| ~ 'E'(f(X1),s(s(s('0')))) ),
inference(spm,[status(thm)],[c_0_53,c_0_37]) ).
cnf(c_0_55,plain,
( ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X1),s(s('0'))) ),
inference(spm,[status(thm)],[c_0_54,c_0_42]) ).
cnf(c_0_56,plain,
~ 'E'(f(X1),s('0')),
inference(spm,[status(thm)],[c_0_55,c_0_46]) ).
cnf(c_0_57,plain,
$false,
inference(sr,[status(thm)],[c_0_50,c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.39 % Computer : n002.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Mon Sep 21 12:09:08 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.16/5.46 % Version: 3.5.1
% 0.16/5.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.46 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.46 % Starting sh5l with 300s (1) cores
% 0.16/5.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3239416 completed with status 0
% 0.16/5.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/5.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.46 % No SInE strategy applied
% 0.16/5.46 % Search class: FHHNM-FFLF21-DFFFFFNN
% 0.16/5.46 % partial match(2): FHUNM-FFSF21-DFFFFFNN
% 0.16/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/5.46 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 300s (1) cores
% 0.16/5.46 % Starting new_bool_3 with 296s (1) cores
% 0.16/5.46 % Starting new_bool_1 with 291s (1) cores
% 0.16/5.46 % SubtermCWHack with pid 3239423 completed with status 0
% 0.16/5.46 % Result found by SubtermCWHack
% 0.16/5.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.46 % No SInE strategy applied
% 0.16/5.46 % Search class: FHHNM-FFLF21-DFFFFFNN
% 0.16/5.46 % partial match(2): FHUNM-FFSF21-DFFFFFNN
% 0.16/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.46 % Preprocessing time : 0.002 s
% 0.16/5.46
% 0.16/5.46 % Proof found!
% 0.16/5.46 % SZS status Unsatisfiable
% 0.16/5.46 % SZS output start CNFRefutation
% See solution above
% 0.16/5.46 % Parsed axioms : 23
% 0.16/5.46 % Removed by relevancy pruning/SinE : 0
% 0.16/5.46 % Initial clauses : 23
% 0.16/5.46 % Removed in clause preprocessing : 0
% 0.16/5.46 % Initial clauses in saturation : 23
% 0.16/5.46 % Processed clauses : 41
% 0.16/5.46 % ...of these trivial : 0
% 0.16/5.46 % ...subsumed : 0
% 0.16/5.46 % ...remaining for further processing : 41
% 0.16/5.46 % Other redundant clauses eliminated : 0
% 0.16/5.46 % Clauses deleted for lack of memory : 0
% 0.16/5.46 % Backward-subsumed : 13
% 0.16/5.46 % Backward-rewritten : 6
% 0.16/5.46 % Generated clauses : 20
% 0.16/5.46 % ...of the previous two non-redundant : 19
% 0.16/5.46 % ...aggressively subsumed : 0
% 0.16/5.46 % Contextual simplify-reflections : 0
% 0.16/5.46 % Paramodulations : 19
% 0.16/5.46 % Factorizations : 0
% 0.16/5.46 % NegExts : 0
% 0.16/5.46 % Equation resolutions : 0
% 0.16/5.46 % Disequality decompositions : 0
% 0.16/5.46 % Total rewrite steps : 94
% 0.16/5.46 % ...of those cached : 64
% 0.16/5.46 % Propositional unsat checks : 0
% 0.16/5.46 % Propositional check models : 0
% 0.16/5.46 % Propositional check unsatisfiable : 0
% 0.16/5.46 % Propositional clauses : 0
% 0.16/5.46 % Propositional clauses after purity: 0
% 0.16/5.46 % Propositional unsat core size : 0
% 0.16/5.46 % Propositional preprocessing time : 0.000
% 0.16/5.46 % Propositional encoding time : 0.000
% 0.16/5.46 % Propositional solver time : 0.000
% 0.16/5.46 % Success case prop preproc time : 0.000
% 0.16/5.46 % Success case prop encoding time : 0.000
% 0.16/5.46 % Success case prop solver time : 0.000
% 0.16/5.46 % Current number of processed clauses : 21
% 0.16/5.46 % Positive orientable unit clauses : 19
% 0.16/5.46 % Positive unorientable unit clauses: 0
% 0.16/5.46 % Negative unit clauses : 2
% 0.16/5.46 % Non-unit-clauses : 0
% 0.16/5.46 % Current number of unprocessed clauses: 1
% 0.16/5.46 % ...number of literals in the above : 11
% 0.16/5.46 % Current number of archived formulas : 0
% 0.16/5.46 % Current number of archived clauses : 20
% 0.16/5.46 % Clause-clause subsumption calls (NU) : 25
% 0.16/5.46 % Rec. Clause-clause subsumption calls : 19
% 0.16/5.46 % Non-unit clause-clause subsumptions : 11
% 0.16/5.46 % Unit Clause-clause subsumption calls : 3
% 0.16/5.46 % Rewrite failures with RHS unbound : 0
% 0.16/5.46 % BW rewrite match attempts : 45
% 0.16/5.46 % BW rewrite match successes : 6
% 0.16/5.46 % Condensation attempts : 0
% 0.16/5.46 % Condensation successes : 0
% 0.16/5.46 % Termbank termtop insertions : 5678
% 0.16/5.46 % Search garbage collected termcells : 182
% 0.16/5.46
% 0.16/5.46 % -------------------------------------------------
% 0.16/5.46 % User time : 0.005 s
% 0.16/5.46 % System time : 0.005 s
% 0.16/5.46 % Total time : 0.010 s
% 0.16/5.46 % Maximum resident set size: 3680 pages
% 0.16/5.46
% 0.16/5.46 % -------------------------------------------------
% 0.16/5.46 % User time : 0.026 s
% 0.16/5.46 % System time : 0.016 s
% 0.16/5.46 % Total time : 0.042 s
% 0.16/5.46 % Maximum resident set size: 4864 pages
% 0.16/5.46 % E exiting
%------------------------------------------------------------------------------