%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL109-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:11:47 PM UTC 2026
% Result : Unsatisfiable 15.74s 2.77s
% Output : CNFRefutation 15.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 6 RR)
% Number of literals : 57 ( 56 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_2,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c_0_5,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_6,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_7,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
cnf(c_0_8,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_9,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_6]) ).
cnf(c_0_10,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_9]) ).
cnf(c_0_11,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_12,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_13,plain,
implies(implies(X1,implies(not(X2),not(X3))),implies(X1,implies(X3,X2))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_6]) ).
cnf(c_0_14,plain,
implies(X1,implies(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_12]),c_0_6]),c_0_6]) ).
cnf(c_0_15,plain,
implies(not(X1),implies(X1,X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_6]) ).
cnf(c_0_16,plain,
implies(not(truth),X1) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_17,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_11,c_0_6]) ).
cnf(c_0_18,plain,
implies(implies(X1,not(truth)),not(truth)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_6]) ).
cnf(c_0_19,plain,
implies(implies(implies(X1,X2),X3),implies(implies(not(X2),not(X1)),X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_6]) ).
cnf(c_0_20,plain,
not(not(truth)) = truth,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_5]),c_0_6]) ).
cnf(c_0_22,plain,
implies(not(not(X1)),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_20]),c_0_6]),c_0_6]) ).
cnf(c_0_23,plain,
implies(implies(X1,X2),implies(implies(not(X1),not(truth)),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_17]),c_0_6]) ).
cnf(c_0_24,plain,
implies(implies(implies(X1,X2),not(truth)),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_16]),c_0_6]) ).
cnf(c_0_25,plain,
implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,X1)),implies(X3,X1)) = implies(implies(X1,X2),implies(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_5]),c_0_6]) ).
cnf(c_0_26,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_6]) ).
cnf(c_0_27,plain,
implies(X1,not(not(X1))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_22]),c_0_6]) ).
cnf(c_0_28,plain,
implies(X1,not(implies(X1,not(truth)))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_18]),c_0_18]) ).
cnf(c_0_29,plain,
implies(not(implies(X1,X2)),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_24]),c_0_20]),c_0_6]),c_0_6]) ).
cnf(c_0_30,plain,
implies(implies(implies(X1,implies(implies(X2,X3),implies(X4,X3))),implies(X1,implies(X4,X2))),implies(X1,implies(X4,X2))) = implies(X1,implies(implies(X2,X3),implies(X4,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_5]),c_0_6]),c_0_6]) ).
cnf(c_0_31,plain,
implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(implies(implies(X3,X2),X2),X1)),implies(implies(implies(X3,X2),X2),X1)) = implies(implies(X1,X2),implies(X3,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
implies(implies(implies(implies(X1,X2),X2),X3),implies(implies(X3,X2),implies(X1,X2))) = truth,
inference(spm,[status(thm)],[c_0_5,c_0_26]) ).
cnf(c_0_33,plain,
implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_6]) ).
cnf(c_0_34,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_27]),c_0_6]),c_0_22]),c_0_6]) ).
cnf(c_0_35,plain,
not(implies(X1,not(truth))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_28]),c_0_6]),c_0_29]),c_0_6]) ).
cnf(c_0_36,plain,
implies(implies(implies(X1,X2),X2),implies(X3,X2)) = implies(X1,implies(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_6]),c_0_33]),c_0_32]),c_0_6]),c_0_6]) ).
cnf(c_0_37,plain,
implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_8]) ).
cnf(c_0_38,plain,
implies(X1,not(truth)) = not(X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
implies(implies(X1,implies(X2,X3)),implies(implies(implies(X3,X2),X2),implies(X1,X3))) = truth,
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_40,plain,
implies(implies(implies(X1,X2),X2),implies(X3,X1)) = implies(X2,implies(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_36]) ).
cnf(c_0_41,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_38]),c_0_38]),c_0_11]),c_0_6]),c_0_38]) ).
cnf(c_0_42,plain,
implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3))) = truth,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_44,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_45,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_42]),c_0_6]),c_0_42]),c_0_6]) ).
cnf(c_0_46,plain,
implies(X1,not(implies(X1,X2))) = implies(X2,not(implies(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_41]),c_0_41]),c_0_43]),c_0_43]) ).
cnf(c_0_47,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(fof_simplification,[status(thm)],[prove_wajsberg_mv_4]) ).
cnf(c_0_48,plain,
implies(implies(implies(X1,implies(implies(X2,X3),X3)),implies(X1,X2)),implies(X1,X2)) = implies(X1,implies(implies(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_7]),c_0_6]),c_0_6]) ).
cnf(c_0_49,plain,
implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
implies(implies(X1,X2),not(implies(implies(X2,X1),X1))) = not(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_7]),c_0_38]),c_0_43]) ).
cnf(c_0_51,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
c_0_47 ).
cnf(c_0_52,plain,
implies(X1,implies(implies(X1,implies(implies(X1,implies(implies(X2,X3),X3)),X2)),X2)) = implies(X1,implies(implies(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_45]),c_0_45]) ).
cnf(c_0_53,plain,
implies(implies(X1,X2),implies(implies(implies(X2,X1),X1),X3)) = implies(X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_34]),c_0_41]) ).
cnf(c_0_54,negated_conjecture,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_45]),c_0_45]) ).
cnf(c_0_55,plain,
implies(X1,implies(implies(X2,X1),X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_9]),c_0_12]),c_0_6]),c_0_45]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_7])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:06:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 15.74/2.77 % Version: 3.5.1
% 15.74/2.77 % Preprocessing class: FSSSSMSSSSSNFFN.
% 15.74/2.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.74/2.77 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 15.74/2.77 % Starting new_bool_3 with 300s (1) cores
% 15.74/2.77 % Starting new_bool_1 with 300s (1) cores
% 15.74/2.77 % Starting sh5l with 300s (1) cores
% 15.74/2.77 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1560326 completed with status 0
% 15.74/2.77 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 15.74/2.77 % Preprocessing class: FSSSSMSSSSSNFFN.
% 15.74/2.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.74/2.77 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 15.74/2.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.74/2.77 % No SInE strategy applied
% 15.74/2.77 % Search class: FUUPM-FFSF21-MFFFFFNN
% 15.74/2.77 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 15.74/2.77 % Starting SubtermCWHack with 136s (1) cores
% 15.74/2.77 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 15.74/2.77 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 15.74/2.77 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 15.74/2.77 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 15.74/2.77 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1560332 completed with status 0
% 15.74/2.77 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 15.74/2.77 % Preprocessing class: FSSSSMSSSSSNFFN.
% 15.74/2.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.74/2.77 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 15.74/2.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.74/2.77 % No SInE strategy applied
% 15.74/2.77 % Search class: FUUPM-FFSF21-MFFFFFNN
% 15.74/2.77 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 15.74/2.77 % Starting SubtermCWHack with 136s (1) cores
% 15.74/2.77 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 15.74/2.77 % Preprocessing time : 0.004 s
% 15.74/2.77
% 15.74/2.77 % Proof found!
% 15.74/2.77 % SZS status Unsatisfiable
% 15.74/2.77 % SZS output start CNFRefutation
% See solution above
% 15.74/2.77 % Parsed axioms : 5
% 15.74/2.77 % Removed by relevancy pruning/SinE : 0
% 15.74/2.77 % Initial clauses : 5
% 15.74/2.77 % Removed in clause preprocessing : 0
% 15.74/2.77 % Initial clauses in saturation : 5
% 15.74/2.77 % Processed clauses : 1366
% 15.74/2.77 % ...of these trivial : 911
% 15.74/2.77 % ...subsumed : 176
% 15.74/2.77 % ...remaining for further processing : 279
% 15.74/2.77 % Other redundant clauses eliminated : 0
% 15.74/2.77 % Clauses deleted for lack of memory : 0
% 15.74/2.77 % Backward-subsumed : 0
% 15.74/2.77 % Backward-rewritten : 88
% 15.74/2.77 % Generated clauses : 123880
% 15.74/2.77 % ...of the previous two non-redundant : 63313
% 15.74/2.77 % ...aggressively subsumed : 0
% 15.74/2.77 % Contextual simplify-reflections : 0
% 15.74/2.77 % Paramodulations : 123880
% 15.74/2.77 % Factorizations : 0
% 15.74/2.77 % NegExts : 0
% 15.74/2.77 % Equation resolutions : 0
% 15.74/2.77 % Disequality decompositions : 0
% 15.74/2.77 % Total rewrite steps : 264084
% 15.74/2.77 % ...of those cached : 214482
% 15.74/2.77 % Propositional unsat checks : 0
% 15.74/2.77 % Propositional check models : 0
% 15.74/2.77 % Propositional check unsatisfiable : 0
% 15.74/2.77 % Propositional clauses : 0
% 15.74/2.77 % Propositional clauses after purity: 0
% 15.74/2.77 % Propositional unsat core size : 0
% 15.74/2.77 % Propositional preprocessing time : 0.000
% 15.74/2.77 % Propositional encoding time : 0.000
% 15.74/2.77 % Propositional solver time : 0.000
% 15.74/2.77 % Success case prop preproc time : 0.000
% 15.74/2.77 % Success case prop encoding time : 0.000
% 15.74/2.77 % Success case prop solver time : 0.000
% 15.74/2.77 % Current number of processed clauses : 191
% 15.74/2.77 % Positive orientable unit clauses : 182
% 15.74/2.77 % Positive unorientable unit clauses: 8
% 15.74/2.77 % Negative unit clauses : 1
% 15.74/2.77 % Non-unit-clauses : 0
% 15.74/2.77 % Current number of unprocessed clauses: 59546
% 15.74/2.77 % ...number of literals in the above : 59546
% 15.74/2.77 % Current number of archived formulas : 0
% 15.74/2.77 % Current number of archived clauses : 88
% 15.74/2.77 % Clause-clause subsumption calls (NU) : 0
% 15.74/2.77 % Rec. Clause-clause subsumption calls : 0
% 15.74/2.77 % Non-unit clause-clause subsumptions : 0
% 15.74/2.77 % Unit Clause-clause subsumption calls : 57
% 15.74/2.77 % Rewrite failures with RHS unbound : 0
% 15.74/2.77 % BW rewrite match attempts : 5604
% 15.74/2.77 % BW rewrite match successes : 288
% 15.74/2.77 % Condensation attempts : 0
% 15.74/2.77 % Condensation successes : 0
% 15.74/2.77 % Termbank termtop insertions : 2033322
% 15.74/2.77 % Search garbage collected termcells : 2
% 15.74/2.77
% 15.74/2.77 % -------------------------------------------------
% 15.74/2.77 % User time : 2.173 s
% 15.74/2.77 % System time : 0.099 s
% 15.74/2.77 % Total time : 2.272 s
% 15.74/2.77 % Maximum resident set size: 3636 pages
% 15.74/2.77
% 15.74/2.77 % -------------------------------------------------
% 15.74/2.77 % User time : 10.634 s
% 15.74/2.77 % System time : 0.429 s
% 15.74/2.77 % Total time : 11.064 s
% 15.74/2.77 % Maximum resident set size: 4608 pages
% 15.74/2.77 % E exiting
%------------------------------------------------------------------------------