%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWX199-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 03:14:43 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of clauses : 54 ( 48 unt; 0 nHn; 12 RR)
% Number of literals : 60 ( 59 equ; 17 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-5 aty)
% Number of variables : 126 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_010,axiom,
prop_merge_comm(X1,X2,X3) = impl(eq(merge(X1,X2),merge(X2,X1)),impl(eq(merge(X1,X3),merge(X3,X1)),eq(merge(X2,X3),merge(X3,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_006,axiom,
merge(cons(X1,X2),nil) = cons(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_005,axiom,
merge(nil,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_016,axiom,
eq(X1,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_008,axiom,
impl(btrue,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_007,axiom,
merge(cons(X1,X2),cons(X3,X4)) = aux(X1,X2,X3,X4,leqNat(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_002,axiom,
leqNat(z,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom,axiom,
aux(X1,X2,X3,X4,btrue) = cons(X1,merge(X2,cons(X3,X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_020,axiom,
( eq2(X1,X2) != btrue
| eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
cnf(goal,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(axiom_017,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
cnf(axiom_003,axiom,
leqNat(s(X1),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom_001,axiom,
aux(X1,X2,X3,X4,bfalse) = cons(X3,merge(cons(X1,X2),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_004,axiom,
leqNat(s(X1),s(X2)) = leqNat(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_019,axiom,
( eq2(X1,X2) != bfalse
| eq(cons(X1,X3),cons(X2,X4)) = bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_018,axiom,
eq3(X1,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
cnf(axiom_014,axiom,
eq2(z,s(X1)) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
cnf(c_0_17,axiom,
prop_merge_comm(X1,X2,X3) = impl(eq(merge(X1,X2),merge(X2,X1)),impl(eq(merge(X1,X3),merge(X3,X1)),eq(merge(X2,X3),merge(X3,X2)))),
axiom_010 ).
cnf(c_0_18,axiom,
merge(cons(X1,X2),nil) = cons(X1,X2),
axiom_006 ).
cnf(c_0_19,axiom,
merge(nil,X1) = X1,
axiom_005 ).
cnf(c_0_20,axiom,
eq(X1,X1) = btrue,
axiom_016 ).
cnf(c_0_21,axiom,
impl(btrue,X1) = X1,
axiom_008 ).
cnf(c_0_22,axiom,
merge(cons(X1,X2),cons(X3,X4)) = aux(X1,X2,X3,X4,leqNat(X1,X3)),
axiom_007 ).
cnf(c_0_23,axiom,
leqNat(z,X1) = btrue,
axiom_002 ).
cnf(c_0_24,axiom,
aux(X1,X2,X3,X4,btrue) = cons(X1,merge(X2,cons(X3,X4))),
axiom ).
cnf(c_0_25,plain,
impl(eq(X1,merge(X1,nil)),eq(merge(X1,cons(X2,X3)),merge(cons(X2,X3),X1))) = prop_merge_comm(nil,X1,cons(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[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]),c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
merge(cons(z,X1),cons(X2,X3)) = cons(z,merge(X1,cons(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
( eq2(X1,X2) != btrue
| eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4) ),
inference(fof_simplification,[status(thm)],[axiom_020]) ).
cnf(c_0_28,plain,
eq(merge(cons(X1,X2),cons(z,X3)),cons(z,merge(X3,cons(X1,X2)))) = prop_merge_comm(nil,cons(X1,X2),cons(z,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]),c_0_20]),c_0_21]) ).
cnf(c_0_29,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_30,plain,
( eq2(X1,X2) != btrue
| eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4) ),
c_0_27 ).
cnf(c_0_31,plain,
eq(cons(z,merge(X1,cons(z,X2))),cons(z,merge(X2,cons(z,X1)))) = prop_merge_comm(nil,cons(z,X1),cons(z,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_32,axiom,
eq2(X1,X1) = btrue,
axiom_017 ).
cnf(c_0_33,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
c_0_29 ).
cnf(c_0_34,plain,
prop_merge_comm(nil,cons(z,X1),cons(z,X2)) = eq(merge(X1,cons(z,X2)),merge(X2,cons(z,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,axiom,
leqNat(s(X1),z) = bfalse,
axiom_003 ).
cnf(c_0_36,axiom,
aux(X1,X2,X3,X4,bfalse) = cons(X3,merge(cons(X1,X2),X4)),
axiom_001 ).
cnf(c_0_37,axiom,
leqNat(s(X1),s(X2)) = leqNat(X1,X2),
axiom_004 ).
cnf(c_0_38,negated_conjecture,
eq3(eq(merge(X1,cons(z,X2)),merge(X2,cons(z,X1))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
merge(cons(s(X1),X2),cons(z,X3)) = cons(z,merge(cons(s(X1),X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_36]) ).
cnf(c_0_40,plain,
aux(s(X1),X2,s(X3),X4,leqNat(X1,X3)) = merge(cons(s(X1),X2),cons(s(X3),X4)),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
eq3(eq(merge(X1,cons(z,cons(s(X2),X3))),cons(z,merge(cons(s(X2),X3),X1))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
merge(cons(s(z),X1),cons(s(X2),X3)) = cons(s(z),merge(X1,cons(s(X2),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_23]),c_0_24]) ).
cnf(c_0_43,negated_conjecture,
eq3(eq(cons(z,merge(cons(s(X1),X2),cons(s(z),X3))),cons(z,cons(s(z),merge(X3,cons(s(X1),X2))))),bfalse) != btrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
eq3(eq(merge(cons(s(X1),X2),cons(s(z),X3)),cons(s(z),merge(X3,cons(s(X1),X2)))),bfalse) != btrue,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_32])]) ).
cnf(c_0_45,negated_conjecture,
eq3(eq(merge(cons(s(X1),X2),cons(s(z),nil)),cons(s(z),cons(s(X1),X2))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_44,c_0_19]) ).
cnf(c_0_46,negated_conjecture,
eq3(eq(cons(s(z),merge(X1,cons(s(z),nil))),cons(s(z),cons(s(z),X1))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
eq3(eq(merge(X1,cons(s(z),nil)),cons(s(z),X1)),bfalse) != btrue,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_30]),c_0_32])]) ).
cnf(c_0_48,plain,
( eq2(X1,X2) != bfalse
| eq(cons(X1,X3),cons(X2,X4)) = bfalse ),
inference(fof_simplification,[status(thm)],[axiom_019]) ).
cnf(c_0_49,negated_conjecture,
eq3(eq(cons(z,merge(X1,cons(s(z),nil))),cons(s(z),cons(z,X1))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_47,c_0_26]) ).
cnf(c_0_50,plain,
( eq2(X1,X2) != bfalse
| eq(cons(X1,X3),cons(X2,X4)) = bfalse ),
c_0_48 ).
cnf(c_0_51,axiom,
eq3(X1,X1) = btrue,
axiom_018 ).
cnf(c_0_52,axiom,
eq2(z,s(X1)) = bfalse,
axiom_014 ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX199-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 10:37:14 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.47 % Version: 3.5.1
% 0.14/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.47 % Starting sh5l with 300s (1) cores
% 0.14/5.47 % sh5l with pid 2217654 completed with status 0
% 0.14/5.47 % Result found by sh5l
% 0.14/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.47 % Starting sh5l with 300s (1) cores
% 0.14/5.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.47 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.47 % Search class: FHUPM-FFMF32-MFFFFFNN
% 0.14/5.47 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.47 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.47 % SubtermCWHack with pid 2217660 completed with status 0
% 0.14/5.47 % Result found by SubtermCWHack
% 0.14/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.47 % Starting sh5l with 300s (1) cores
% 0.14/5.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.47 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.47 % Search class: FHUPM-FFMF32-MFFFFFNN
% 0.14/5.47 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.47 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.47 % Preprocessing time : 0.001 s
% 0.14/5.47
% 0.14/5.47 % Proof found!
% 0.14/5.47 % SZS status Unsatisfiable
% 0.14/5.47 % SZS output start CNFRefutation
% See solution above
% 0.14/5.47 % Parsed axioms : 24
% 0.14/5.47 % Removed by relevancy pruning/SinE : 0
% 0.14/5.47 % Initial clauses : 24
% 0.14/5.47 % Removed in clause preprocessing : 0
% 0.14/5.47 % Initial clauses in saturation : 24
% 0.14/5.47 % Processed clauses : 491
% 0.14/5.47 % ...of these trivial : 102
% 0.14/5.47 % ...subsumed : 181
% 0.14/5.47 % ...remaining for further processing : 208
% 0.14/5.47 % Other redundant clauses eliminated : 0
% 0.14/5.47 % Clauses deleted for lack of memory : 0
% 0.14/5.47 % Backward-subsumed : 3
% 0.14/5.47 % Backward-rewritten : 35
% 0.14/5.47 % Generated clauses : 1843
% 0.14/5.47 % ...of the previous two non-redundant : 1604
% 0.14/5.47 % ...aggressively subsumed : 0
% 0.14/5.47 % Contextual simplify-reflections : 0
% 0.14/5.47 % Paramodulations : 1843
% 0.14/5.47 % Factorizations : 0
% 0.14/5.47 % NegExts : 0
% 0.14/5.47 % Equation resolutions : 0
% 0.14/5.47 % Disequality decompositions : 0
% 0.14/5.47 % Total rewrite steps : 3869
% 0.14/5.47 % ...of those cached : 3250
% 0.14/5.47 % Propositional unsat checks : 0
% 0.14/5.47 % Propositional check models : 0
% 0.14/5.47 % Propositional check unsatisfiable : 0
% 0.14/5.47 % Propositional clauses : 0
% 0.14/5.47 % Propositional clauses after purity: 0
% 0.14/5.47 % Propositional unsat core size : 0
% 0.14/5.47 % Propositional preprocessing time : 0.000
% 0.14/5.47 % Propositional encoding time : 0.000
% 0.14/5.47 % Propositional solver time : 0.000
% 0.14/5.47 % Success case prop preproc time : 0.000
% 0.14/5.47 % Success case prop encoding time : 0.000
% 0.14/5.47 % Success case prop solver time : 0.000
% 0.14/5.47 % Current number of processed clauses : 170
% 0.14/5.47 % Positive orientable unit clauses : 126
% 0.14/5.47 % Positive unorientable unit clauses: 5
% 0.14/5.47 % Negative unit clauses : 36
% 0.14/5.47 % Non-unit-clauses : 3
% 0.14/5.47 % Current number of unprocessed clauses: 1126
% 0.14/5.47 % ...number of literals in the above : 1131
% 0.14/5.47 % Current number of archived formulas : 0
% 0.14/5.47 % Current number of archived clauses : 38
% 0.14/5.47 % Clause-clause subsumption calls (NU) : 6
% 0.14/5.47 % Rec. Clause-clause subsumption calls : 6
% 0.14/5.47 % Non-unit clause-clause subsumptions : 4
% 0.14/5.47 % Unit Clause-clause subsumption calls : 817
% 0.14/5.47 % Rewrite failures with RHS unbound : 0
% 0.14/5.47 % BW rewrite match attempts : 280
% 0.14/5.47 % BW rewrite match successes : 45
% 0.14/5.47 % Condensation attempts : 0
% 0.14/5.47 % Condensation successes : 0
% 0.14/5.47 % Termbank termtop insertions : 66062
% 0.14/5.47 % Search garbage collected termcells : 8
% 0.14/5.47
% 0.14/5.47 % -------------------------------------------------
% 0.14/5.47 % User time : 0.028 s
% 0.14/5.47 % System time : 0.005 s
% 0.14/5.47 % Total time : 0.032 s
% 0.14/5.47 % Maximum resident set size: 3644 pages
% 0.14/5.47
% 0.14/5.47 % -------------------------------------------------
% 0.14/5.47 % User time : 0.030 s
% 0.14/5.47 % System time : 0.009 s
% 0.14/5.47 % Total time : 0.039 s
% 0.14/5.47 % Maximum resident set size: 4864 pages
% 0.14/5.47 % E exiting
%------------------------------------------------------------------------------