%------------------------------------------------------------------------------
% 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 : Unsatisfiable 0.28s 0.68s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 52 ( 46 unt; 0 nHn; 9 RR)
% Number of literals : 58 ( 57 equ; 14 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 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 : 125 ( 24 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/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_006,axiom,
merge(cons(X1,X2),nil) = cons(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_005,axiom,
merge(nil,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_016,axiom,
eq(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_008,axiom,
impl(btrue,X1) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_002,axiom,
leqNat(z,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom,axiom,
aux(X1,X2,X3,X4,btrue) = cons(X1,merge(X2,cons(X3,X4))),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(axiom_017,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
cnf(goal,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(axiom_003,axiom,
leqNat(s(X1),z) = bfalse,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_004,axiom,
leqNat(s(X1),s(X2)) = leqNat(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_019,axiom,
( eq2(X1,X2) != bfalse
| eq(cons(X1,X3),cons(X2,X4)) = bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_014,axiom,
eq2(z,s(X1)) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
cnf(axiom_018,axiom,
eq3(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
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,
( eq2(X1,X2) != btrue
| eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4) ),
inference(fof_simplification,[status(thm)],[axiom_020]) ).
cnf(c_0_26,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_27,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_28,plain,
( eq2(X1,X2) != btrue
| eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4) ),
c_0_25 ).
cnf(c_0_29,axiom,
eq2(X1,X1) = btrue,
axiom_017 ).
cnf(c_0_30,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_31,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_26,c_0_27]),c_0_18]),c_0_20]),c_0_21]) ).
cnf(c_0_32,plain,
eq(cons(X1,X2),cons(X1,X3)) = eq(X2,X3),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
c_0_30 ).
cnf(c_0_34,plain,
eq(merge(X1,cons(z,X2)),merge(X2,cons(z,X1))) = prop_merge_comm(nil,cons(z,X1),cons(z,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),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(merge(cons(s(X1),X2),cons(s(z),X3)),cons(s(z),merge(X3,cons(s(X1),X2)))),bfalse) != btrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_39]),c_0_32]) ).
cnf(c_0_44,plain,
( eq2(X1,X2) != bfalse
| eq(cons(X1,X3),cons(X2,X4)) = bfalse ),
inference(fof_simplification,[status(thm)],[axiom_019]) ).
cnf(c_0_45,negated_conjecture,
eq3(eq(merge(X1,cons(s(z),X2)),merge(X2,cons(s(z),X1))),bfalse) != btrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_32]) ).
cnf(c_0_46,plain,
( eq2(X1,X2) != bfalse
| eq(cons(X1,X3),cons(X2,X4)) = bfalse ),
c_0_44 ).
cnf(c_0_47,axiom,
eq2(z,s(X1)) = bfalse,
axiom_014 ).
cnf(c_0_48,negated_conjecture,
eq3(eq(merge(X1,cons(s(z),nil)),cons(s(z),X1)),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_45,c_0_19]) ).
cnf(c_0_49,plain,
eq(cons(z,X1),cons(s(X2),X3)) = bfalse,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,axiom,
eq3(X1,X1) = btrue,
axiom_018 ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_27]),c_0_49]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX199-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.48 % Computer : n017.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 10:27:43 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.19/0.49 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.57 Running first-order theorem proving
% 0.23/0.57 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
% 0.28/0.68 % Version: 3.5.1
% 0.28/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.68 % Starting sh5l with 300s (1) cores
% 0.28/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2097722 completed with status 0
% 0.28/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.28/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.68 % No SInE strategy applied
% 0.28/0.68 % Search class: FHUPM-FFMF32-MFFFFFNN
% 0.28/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.28/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 226s (1) cores
% 0.28/0.68 % Starting new_bool_3 with 226s (1) cores
% 0.28/0.68 % Starting new_bool_1 with 226s (1) cores
% 0.28/0.68 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 2097726 completed with status 0
% 0.28/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 0.28/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.68 % No SInE strategy applied
% 0.28/0.68 % Search class: FHUPM-FFMF32-MFFFFFNN
% 0.28/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.28/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 226s (1) cores
% 0.28/0.68 % Preprocessing time : 0.002 s
% 0.28/0.68 % Presaturation interreduction done
% 0.28/0.68
% 0.28/0.68 % Proof found!
% 0.28/0.68 % SZS status Unsatisfiable
% 0.28/0.68 % SZS output start CNFRefutation
% See solution above
% 0.28/0.68 % Parsed axioms : 24
% 0.28/0.68 % Removed by relevancy pruning/SinE : 0
% 0.28/0.68 % Initial clauses : 24
% 0.28/0.68 % Removed in clause preprocessing : 0
% 0.28/0.68 % Initial clauses in saturation : 24
% 0.28/0.68 % Processed clauses : 356
% 0.28/0.68 % ...of these trivial : 46
% 0.28/0.68 % ...subsumed : 111
% 0.28/0.68 % ...remaining for further processing : 199
% 0.28/0.68 % Other redundant clauses eliminated : 0
% 0.28/0.68 % Clauses deleted for lack of memory : 0
% 0.28/0.68 % Backward-subsumed : 4
% 0.28/0.68 % Backward-rewritten : 24
% 0.28/0.68 % Generated clauses : 945
% 0.28/0.68 % ...of the previous two non-redundant : 765
% 0.28/0.68 % ...aggressively subsumed : 0
% 0.28/0.68 % Contextual simplify-reflections : 0
% 0.28/0.68 % Paramodulations : 945
% 0.28/0.68 % Factorizations : 0
% 0.28/0.68 % NegExts : 0
% 0.28/0.68 % Equation resolutions : 0
% 0.28/0.68 % Disequality decompositions : 0
% 0.28/0.68 % Total rewrite steps : 2612
% 0.28/0.68 % ...of those cached : 2111
% 0.28/0.68 % Propositional unsat checks : 0
% 0.28/0.68 % Propositional check models : 0
% 0.28/0.68 % Propositional check unsatisfiable : 0
% 0.28/0.68 % Propositional clauses : 0
% 0.28/0.68 % Propositional clauses after purity: 0
% 0.28/0.68 % Propositional unsat core size : 0
% 0.28/0.68 % Propositional preprocessing time : 0.000
% 0.28/0.68 % Propositional encoding time : 0.000
% 0.28/0.68 % Propositional solver time : 0.000
% 0.28/0.68 % Success case prop preproc time : 0.000
% 0.28/0.68 % Success case prop encoding time : 0.000
% 0.28/0.68 % Success case prop solver time : 0.000
% 0.28/0.68 % Current number of processed clauses : 147
% 0.28/0.68 % Positive orientable unit clauses : 112
% 0.28/0.68 % Positive unorientable unit clauses: 3
% 0.28/0.68 % Negative unit clauses : 15
% 0.28/0.68 % Non-unit-clauses : 17
% 0.28/0.68 % Current number of unprocessed clauses: 454
% 0.28/0.68 % ...number of literals in the above : 456
% 0.28/0.68 % Current number of archived formulas : 0
% 0.28/0.68 % Current number of archived clauses : 52
% 0.28/0.68 % Clause-clause subsumption calls (NU) : 84
% 0.28/0.68 % Rec. Clause-clause subsumption calls : 84
% 0.28/0.68 % Non-unit clause-clause subsumptions : 10
% 0.28/0.68 % Unit Clause-clause subsumption calls : 220
% 0.28/0.68 % Rewrite failures with RHS unbound : 0
% 0.28/0.68 % BW rewrite match attempts : 299
% 0.28/0.68 % BW rewrite match successes : 28
% 0.28/0.68 % Condensation attempts : 0
% 0.28/0.68 % Condensation successes : 0
% 0.28/0.68 % Termbank termtop insertions : 29127
% 0.28/0.68 % Search garbage collected termcells : 8
% 0.28/0.68
% 0.28/0.68 % -------------------------------------------------
% 0.28/0.68 % User time : 0.053 s
% 0.28/0.68 % System time : 0.006 s
% 0.28/0.68 % Total time : 0.060 s
% 0.28/0.68 % Maximum resident set size: 3388 pages
% 0.28/0.68
% 0.28/0.68 % -------------------------------------------------
% 0.28/0.68 % User time : 0.200 s
% 0.28/0.68 % System time : 0.030 s
% 0.28/0.68 % Total time : 0.231 s
% 0.28/0.68 % Maximum resident set size: 4864 pages
% 0.28/0.68 % E exiting
%------------------------------------------------------------------------------