%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 03:14:14 PM UTC 2026
% Result : Theorem 0.22s 10.54s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 41 unt; 0 def)
% Number of atoms : 89 ( 62 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 27 ~; 19 |; 1 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 131 ( 7 sgn 49 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_013,conjecture,
? [X6,X8,X9] :
~ ( merge(X6,X8) = merge(X8,X6)
=> ( merge(X6,X9) = merge(X9,X6)
=> merge(X8,X9) = merge(X9,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_013) ).
fof(axiom_010,axiom,
! [X4,X6] : merge(cons(X4,X6),nil) = cons(X4,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(axiom_009,axiom,
! [X3] : merge(nil,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(axiom_011,axiom,
! [X4,X6,X7,X8] :
( leqNat(X4,X7)
=> merge(cons(X4,X6),cons(X7,X8)) = cons(X4,merge(X6,cons(X7,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(axiom_006,axiom,
! [X3] : leqNat(z,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(axiom_002,axiom,
! [X1,X2] : tail(cons(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(axiom_012,axiom,
! [X4,X6,X7,X8] :
( ~ leqNat(X4,X7)
=> merge(cons(X4,X6),cons(X7,X8)) = cons(X7,merge(cons(X4,X6),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(axiom_008,axiom,
! [X4,X5] :
( leqNat(s(X4),s(X5))
<=> leqNat(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_007,axiom,
! [X4] : ~ leqNat(s(X4),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(axiom_005,axiom,
! [X1] : z != s(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(axiom_001,axiom,
! [X1,X2] : head(cons(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(c_0_11,negated_conjecture,
~ ? [X6,X8,X9] :
~ ( merge(X6,X8) = merge(X8,X6)
=> ( merge(X6,X9) = merge(X9,X6)
=> merge(X8,X9) = merge(X9,X8) ) ),
inference(assume_negation,[status(cth)],[goal_013]) ).
fof(c_0_12,negated_conjecture,
! [X33,X34,X35] :
( merge(X34,X35) = merge(X35,X34)
| merge(X33,X35) != merge(X35,X33)
| merge(X33,X34) != merge(X34,X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_13,plain,
! [X23,X24] : merge(cons(X23,X24),nil) = cons(X23,X24),
inference(variable_rename,[status(thm)],[axiom_010]) ).
fof(c_0_14,plain,
! [X22] : merge(nil,X22) = X22,
inference(variable_rename,[status(thm)],[axiom_009]) ).
fof(c_0_15,plain,
! [X25,X26,X27,X28] :
( merge(cons(X25,X26),cons(X27,X28)) = cons(X25,merge(X26,cons(X27,X28)))
| ~ leqNat(X25,X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_011])])]) ).
fof(c_0_16,plain,
! [X18] : leqNat(z,X18),
inference(variable_rename,[status(thm)],[axiom_006]) ).
cnf(c_0_17,negated_conjecture,
( merge(X1,X3) != merge(X3,X1)
| merge(X1,X2) != merge(X2,X1)
| merge(X2,X3) = merge(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
merge(cons(X1,X2),nil) = cons(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
merge(nil,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ leqNat(X1,X2)
| merge(cons(X1,X3),cons(X2,X4)) = cons(X1,merge(X3,cons(X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
leqNat(z,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( merge(X1,nil) != X1
| merge(X1,cons(X2,X3)) = merge(cons(X2,X3),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_19])]) ).
cnf(c_0_23,plain,
merge(cons(z,X1),cons(X2,X3)) = cons(z,merge(X1,cons(X2,X3))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
merge(cons(X1,X2),cons(X3,X4)) = merge(cons(X3,X4),cons(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
fof(c_0_25,plain,
! [X12,X13] : tail(cons(X12,X13)) = X13,
inference(variable_rename,[status(thm)],[axiom_002]) ).
cnf(c_0_26,negated_conjecture,
merge(cons(X1,X2),cons(z,X3)) = cons(z,merge(X3,cons(X1,X2))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_27,plain,
! [X4,X6,X7,X8] :
( ~ leqNat(X4,X7)
=> merge(cons(X4,X6),cons(X7,X8)) = cons(X7,merge(cons(X4,X6),X8)) ),
inference(fof_simplification,[status(thm)],[axiom_012]) ).
cnf(c_0_28,plain,
tail(cons(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
cons(z,merge(X1,cons(z,X2))) = cons(z,merge(X2,cons(z,X1))),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
fof(c_0_30,plain,
! [X20,X21] :
( ( leqNat(s(X20),s(X21))
| ~ leqNat(X20,X21) )
& ( leqNat(X20,X21)
| ~ leqNat(s(X20),s(X21)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_008])])]) ).
fof(c_0_31,plain,
! [X29,X30,X31,X32] :
( merge(cons(X29,X30),cons(X31,X32)) = cons(X31,merge(cons(X29,X30),X32))
| leqNat(X29,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
cnf(c_0_32,negated_conjecture,
merge(X1,cons(z,X2)) = merge(X2,cons(z,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_28]) ).
cnf(c_0_33,plain,
( ~ leqNat(X1,X2)
| leqNat(s(X1),s(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X4] : ~ leqNat(s(X4),z),
inference(fof_simplification,[status(thm)],[axiom_007]) ).
cnf(c_0_35,plain,
( merge(cons(X1,X3),cons(X2,X4)) = cons(X2,merge(cons(X1,X3),X4))
| leqNat(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
merge(X1,cons(z,cons(X2,X3))) = cons(z,merge(X1,cons(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_32]),c_0_23]) ).
cnf(c_0_37,plain,
leqNat(s(z),s(X1)),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
fof(c_0_38,plain,
! [X19] : ~ leqNat(s(X19),z),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
cnf(c_0_39,negated_conjecture,
( leqNat(X2,z)
| cons(z,merge(X1,cons(X2,X3))) = cons(z,merge(cons(X2,X3),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_36]) ).
cnf(c_0_40,plain,
merge(cons(s(z),X1),cons(s(X2),X3)) = cons(s(z),merge(X1,cons(s(X2),X3))),
inference(spm,[status(thm)],[c_0_20,c_0_37]) ).
cnf(c_0_41,plain,
~ leqNat(s(X1),z),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( merge(X2,nil) != X2
| merge(X2,X1) != merge(X1,X2)
| merge(X1,nil) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( leqNat(X2,z)
| merge(X1,cons(X2,X3)) = merge(cons(X2,X3),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_28]) ).
cnf(c_0_44,negated_conjecture,
cons(z,merge(cons(s(X1),X2),cons(s(z),X3))) = cons(z,cons(s(z),merge(X3,cons(s(X1),X2)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( leqNat(X2,z)
| merge(X1,nil) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_18])]) ).
cnf(c_0_46,negated_conjecture,
merge(cons(s(X1),X2),cons(s(z),X3)) = cons(s(z),merge(X3,cons(s(X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_44]),c_0_28]) ).
cnf(c_0_47,negated_conjecture,
( merge(X1,nil) != X1
| merge(X2,nil) != X2
| merge(X1,X2) = merge(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_19]) ).
cnf(c_0_48,negated_conjecture,
merge(X1,nil) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
cons(s(z),merge(X1,cons(s(z),X2))) = cons(s(z),merge(X2,cons(s(z),X1))),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
merge(X1,X2) = merge(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48])]) ).
cnf(c_0_51,negated_conjecture,
merge(X1,cons(s(z),X2)) = merge(X2,cons(s(z),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_49]),c_0_28]) ).
fof(c_0_52,plain,
! [X1] : z != s(X1),
inference(fof_simplification,[status(thm)],[axiom_005]) ).
fof(c_0_53,plain,
! [X10,X11] : head(cons(X10,X11)) = X10,
inference(variable_rename,[status(thm)],[axiom_001]) ).
cnf(c_0_54,negated_conjecture,
merge(cons(z,X1),X2) = merge(X1,cons(z,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
merge(X1,cons(s(z),nil)) = cons(s(z),X1),
inference(spm,[status(thm)],[c_0_19,c_0_51]) ).
fof(c_0_56,plain,
! [X17] : z != s(X17),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_52])]) ).
cnf(c_0_57,plain,
head(cons(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,negated_conjecture,
cons(s(z),cons(z,X1)) = cons(z,cons(s(z),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_36]),c_0_55]) ).
cnf(c_0_59,plain,
z != s(X1),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_57]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX199+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/10.46 % Computer : n017.cluster.edu
% 0.18/10.46 % Model : x86_64 x86_64
% 0.18/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.46 % Memory : 8046.5625MB
% 0.18/10.46 % OS : Linux 6.8.0-71-generic
% 0.18/10.46 % CPULimit : 300
% 0.18/10.46 % WCLimit : 300
% 0.18/10.46 % DateTime : Mon Sep 21 10:28:07 UTC 2026
% 0.18/10.46 % CPUTime :
% 0.18/10.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/10.50 Running first-order theorem proving
% 0.22/10.50 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
% 0.22/10.54 % Version: 3.5.1
% 0.22/10.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.54 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.54 % Starting new_bool_1 with 300s (1) cores
% 0.22/10.54 % Starting sh5l with 300s (1) cores
% 0.22/10.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2098272 completed with status 0
% 0.22/10.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/10.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/10.54 % No SInE strategy applied
% 0.22/10.54 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.22/10.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/10.54 % Starting SubtermCWHack with 136s (1) cores
% 0.22/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/10.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.22/10.54 % Starting new_bool_3 with 136s (1) cores
% 0.22/10.54 % Starting new_bool_1 with 136s (1) cores
% 0.22/10.54 % new_bool_3 with pid 2098282 completed with status 0
% 0.22/10.54 % Result found by new_bool_3
% 0.22/10.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/10.54 % No SInE strategy applied
% 0.22/10.54 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.22/10.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/10.54 % Starting SubtermCWHack with 136s (1) cores
% 0.22/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/10.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.22/10.54 % Starting new_bool_3 with 136s (1) cores
% 0.22/10.54 % Preprocessing time : 0.001 s
% 0.22/10.54 % Presaturation interreduction done
% 0.22/10.54
% 0.22/10.54 % Proof found!
% 0.22/10.54 % SZS status Theorem
% 0.22/10.54 % SZS output start CNFRefutation
% See solution above
% 0.22/10.54 % Parsed axioms : 13
% 0.22/10.54 % Removed by relevancy pruning/SinE : 0
% 0.22/10.54 % Initial clauses : 14
% 0.22/10.54 % Removed in clause preprocessing : 0
% 0.22/10.54 % Initial clauses in saturation : 14
% 0.22/10.54 % Processed clauses : 190
% 0.22/10.54 % ...of these trivial : 27
% 0.22/10.54 % ...subsumed : 77
% 0.22/10.54 % ...remaining for further processing : 86
% 0.22/10.54 % Other redundant clauses eliminated : 0
% 0.22/10.54 % Clauses deleted for lack of memory : 0
% 0.22/10.54 % Backward-subsumed : 12
% 0.22/10.54 % Backward-rewritten : 25
% 0.22/10.54 % Generated clauses : 1011
% 0.22/10.54 % ...of the previous two non-redundant : 509
% 0.22/10.54 % ...aggressively subsumed : 0
% 0.22/10.54 % Contextual simplify-reflections : 0
% 0.22/10.54 % Paramodulations : 1002
% 0.22/10.54 % Factorizations : 0
% 0.22/10.54 % NegExts : 0
% 0.22/10.54 % Equation resolutions : 8
% 0.22/10.54 % Disequality decompositions : 0
% 0.22/10.54 % Total rewrite steps : 1520
% 0.22/10.54 % ...of those cached : 1220
% 0.22/10.54 % Propositional unsat checks : 0
% 0.22/10.54 % Propositional check models : 0
% 0.22/10.54 % Propositional check unsatisfiable : 0
% 0.22/10.54 % Propositional clauses : 0
% 0.22/10.54 % Propositional clauses after purity: 0
% 0.22/10.54 % Propositional unsat core size : 0
% 0.22/10.54 % Propositional preprocessing time : 0.000
% 0.22/10.54 % Propositional encoding time : 0.000
% 0.22/10.54 % Propositional solver time : 0.000
% 0.22/10.54 % Success case prop preproc time : 0.000
% 0.22/10.54 % Success case prop encoding time : 0.000
% 0.22/10.54 % Success case prop solver time : 0.000
% 0.22/10.54 % Current number of processed clauses : 34
% 0.22/10.54 % Positive orientable unit clauses : 23
% 0.22/10.54 % Positive unorientable unit clauses: 3
% 0.22/10.54 % Negative unit clauses : 3
% 0.22/10.54 % Non-unit-clauses : 5
% 0.22/10.54 % Current number of unprocessed clauses: 213
% 0.22/10.54 % ...number of literals in the above : 390
% 0.22/10.54 % Current number of archived formulas : 0
% 0.22/10.54 % Current number of archived clauses : 52
% 0.22/10.54 % Clause-clause subsumption calls (NU) : 273
% 0.22/10.54 % Rec. Clause-clause subsumption calls : 262
% 0.22/10.54 % Non-unit clause-clause subsumptions : 51
% 0.22/10.54 % Unit Clause-clause subsumption calls : 46
% 0.22/10.54 % Rewrite failures with RHS unbound : 0
% 0.22/10.54 % BW rewrite match attempts : 189
% 0.22/10.54 % BW rewrite match successes : 133
% 0.22/10.54 % Condensation attempts : 0
% 0.22/10.54 % Condensation successes : 0
% 0.22/10.54 % Termbank termtop insertions : 19649
% 0.22/10.54 % Search garbage collected termcells : 84
% 0.22/10.54
% 0.22/10.54 % -------------------------------------------------
% 0.22/10.54 % User time : 0.020 s
% 0.22/10.54 % System time : 0.004 s
% 0.22/10.54 % Total time : 0.024 s
% 0.22/10.54 % Maximum resident set size: 3640 pages
% 0.22/10.54
% 0.22/10.54 % -------------------------------------------------
% 0.22/10.54 % User time : 0.096 s
% 0.22/10.54 % System time : 0.013 s
% 0.22/10.54 % Total time : 0.109 s
% 0.22/10.54 % Maximum resident set size: 4864 pages
% 0.22/10.54 % E exiting
%------------------------------------------------------------------------------