%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:18:35 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 9 RR)
% Number of literals : 40 ( 39 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_2,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
cnf(big_hat_definition,axiom,
big_hat(X1,X2) = not(big_V(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_hat_definition) ).
cnf(big_V_definition,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
cnf(c_0_7,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_8,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_9,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_10,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_10]),c_0_8]) ).
cnf(c_0_13,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_15,plain,
implies(X1,implies(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_8]),c_0_8]) ).
cnf(c_0_16,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_17,plain,
implies(implies(implies(X1,X2),X3),implies(X2,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_15]),c_0_8]) ).
cnf(c_0_18,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_15]),c_0_8]) ).
cnf(c_0_19,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_20,plain,
implies(not(X1),implies(X1,X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_8]) ).
cnf(c_0_21,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_8]) ).
cnf(c_0_22,plain,
implies(not(not(not(truth))),not(truth)) = truth,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
implies(implies(not(X1),not(implies(X2,X1))),implies(implies(X1,X2),X2)) = truth,
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_24,plain,
implies(not(truth),X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_8]) ).
cnf(c_0_25,plain,
not(not(truth)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_8]),c_0_8]) ).
cnf(c_0_26,plain,
implies(not(implies(X1,not(truth))),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_8]),c_0_8]) ).
cnf(c_0_27,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
inference(fof_simplification,[status(thm)],[prove_wajsberg_theorem]) ).
cnf(c_0_28,axiom,
big_hat(X1,X2) = not(big_V(not(X1),not(X2))),
big_hat_definition ).
cnf(c_0_29,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
big_V_definition ).
cnf(c_0_30,plain,
implies(X1,implies(not(X1),not(truth))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_26]),c_0_8]) ).
cnf(c_0_31,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
c_0_27 ).
cnf(c_0_32,plain,
big_hat(X1,X2) = not(implies(implies(not(X1),not(X2)),not(X2))),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
implies(not(X1),not(truth)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_30]),c_0_8]),c_0_19]),c_0_8]) ).
cnf(c_0_34,negated_conjecture,
not(not(implies(implies(not(x),not(y)),not(y)))) != implies(implies(not(x),not(y)),not(y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_32]) ).
cnf(c_0_35,plain,
implies(implies(X1,not(truth)),not(truth)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_24]),c_0_8]) ).
cnf(c_0_36,plain,
implies(X1,not(truth)) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_33]),c_0_24]),c_0_8]) ).
cnf(c_0_37,negated_conjecture,
not(not(implies(implies(not(y),not(x)),not(x)))) != implies(implies(not(y),not(x)),not(x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_9]),c_0_9]) ).
cnf(c_0_38,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:05:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3931665 completed with status 0
% 0.13/0.42 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.13/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.13/0.42 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.42 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.13/0.42 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.13/0.42 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 3931673 completed with status 0
% 0.13/0.42 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.13/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.13/0.42 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.42 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 9
% 0.13/0.42 % Removed by relevancy pruning/SinE : 0
% 0.13/0.42 % Initial clauses : 9
% 0.13/0.42 % Removed in clause preprocessing : 2
% 0.13/0.42 % Initial clauses in saturation : 7
% 0.13/0.42 % Processed clauses : 58
% 0.13/0.42 % ...of these trivial : 21
% 0.13/0.42 % ...subsumed : 2
% 0.13/0.42 % ...remaining for further processing : 35
% 0.13/0.42 % Other redundant clauses eliminated : 0
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 0
% 0.13/0.42 % Backward-rewritten : 15
% 0.13/0.42 % Generated clauses : 583
% 0.13/0.42 % ...of the previous two non-redundant : 238
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 0
% 0.13/0.42 % Paramodulations : 583
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 0
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 843
% 0.13/0.42 % ...of those cached : 643
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 20
% 0.13/0.42 % Positive orientable unit clauses : 17
% 0.13/0.42 % Positive unorientable unit clauses: 1
% 0.13/0.42 % Negative unit clauses : 0
% 0.13/0.42 % Non-unit-clauses : 2
% 0.13/0.42 % Current number of unprocessed clauses: 168
% 0.13/0.42 % ...number of literals in the above : 168
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 17
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 0
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 0
% 0.13/0.42 % Non-unit clause-clause subsumptions : 0
% 0.13/0.42 % Unit Clause-clause subsumption calls : 1
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 53
% 0.13/0.42 % BW rewrite match successes : 16
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 5442
% 0.13/0.42 % Search garbage collected termcells : 6
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.006 s
% 0.13/0.42 % System time : 0.001 s
% 0.13/0.42 % Total time : 0.007 s
% 0.13/0.42 % Maximum resident set size: 3640 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.024 s
% 0.13/0.42 % System time : 0.012 s
% 0.13/0.42 % Total time : 0.036 s
% 0.13/0.42 % Maximum resident set size: 4864 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------