%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL109-3 : 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 : n005.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 01:18:29 PM UTC 2026
% Result : Unsatisfiable 2.29s 0.77s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 39 ( 26 unt; 0 nHn; 18 RR)
% Number of literals : 52 ( 51 equ; 18 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lemma_5,axiom,
( implies(X1,X2) != implies(X2,X3)
| implies(X1,X3) = truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_5) ).
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(lemma_4,axiom,
implies(X1,implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(lemma_2,axiom,
( implies(X1,X2) != implies(X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_2) ).
cnf(lemma_1,axiom,
implies(X1,X1) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
cnf(lemma_7,axiom,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(lemma_6,axiom,
implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_6) ).
cnf(c_0_9,plain,
( implies(X1,X2) != implies(X2,X3)
| implies(X1,X3) = truth ),
inference(fof_simplification,[status(thm)],[lemma_5]) ).
cnf(c_0_10,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_11,axiom,
implies(X1,implies(X2,X1)) = truth,
lemma_4 ).
cnf(c_0_12,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_13,plain,
( implies(X1,X2) != implies(X2,X3)
| implies(X1,X3) = truth ),
c_0_9 ).
cnf(c_0_14,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_15,plain,
( implies(X1,X2) != implies(X2,X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[lemma_2]) ).
cnf(c_0_16,axiom,
implies(X1,X1) = truth,
lemma_1 ).
cnf(c_0_17,axiom,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
lemma_7 ).
cnf(c_0_18,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_19,axiom,
implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2))) = truth,
lemma_6 ).
cnf(c_0_20,plain,
( implies(implies(X3,X1),X2) != truth
| implies(X1,X2) = truth ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_21,plain,
( implies(X1,X2) != implies(X2,X3)
| implies(implies(implies(X1,X2),X2),X3) = truth ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,plain,
( implies(X1,X2) != implies(X2,X1)
| X1 = X2 ),
c_0_15 ).
cnf(c_0_23,plain,
implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_24,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
c_0_18 ).
cnf(c_0_26,plain,
( implies(X2,X1) != X2
| X1 = truth ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_12]),c_0_12]) ).
cnf(c_0_27,plain,
implies(implies(X1,X2),implies(X3,implies(implies(X3,X1),X2))) = truth,
inference(rw,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_28,plain,
( implies(X3,X1) != implies(X1,X2)
| implies(X1,X2) = truth ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
( implies(X2,X1) != truth
| implies(implies(X1,X2),X2) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_17]),c_0_17]) ).
cnf(c_0_31,plain,
( implies(X2,X3) != truth
| implies(X1,implies(implies(X1,X2),X3)) = truth ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( implies(X1,implies(X1,X2)) != truth
| implies(X1,X2) = truth ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_33,plain,
implies(implies(implies(X1,X2),X2),implies(X3,implies(implies(X3,implies(X2,X1)),X1))) = truth,
inference(spm,[status(thm)],[c_0_27,c_0_10]) ).
cnf(c_0_34,plain,
implies(implies(implies(X1,X2),X2),implies(X3,X1)) = implies(X3,implies(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_35,plain,
implies(implies(implies(X1,X2),X3),X3) = implies(X1,implies(implies(X1,implies(X3,X2)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_17]) ).
cnf(c_0_36,negated_conjecture,
implies(implies(implies(a,b),a),a) != truth,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
implies(implies(implies(X1,X2),X1),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_34]),c_0_17]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:05:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 2.29/0.77 % Version: 3.5.1
% 2.29/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.29/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.29/0.77 % Starting new_bool_3 with 300s (1) cores
% 2.29/0.77 % Starting new_bool_1 with 300s (1) cores
% 2.29/0.77 % Starting sh5l with 300s (1) cores
% 2.29/0.77 % new_bool_3 with pid 2114936 completed with status 0
% 2.29/0.77 % Result found by new_bool_3
% 2.29/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.29/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.29/0.77 % Starting new_bool_3 with 300s (1) cores
% 2.29/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.29/0.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.29/0.77 % Search class: FHUPM-FFSF22-MFFFFFNN
% 2.29/0.77 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.29/0.77 % Starting SubtermCWHack with 31s (1) cores
% 2.29/0.77 % SubtermCWHack with pid 2114942 completed with status 0
% 2.29/0.77 % Result found by SubtermCWHack
% 2.29/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.29/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.29/0.77 % Starting new_bool_3 with 300s (1) cores
% 2.29/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.29/0.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.29/0.77 % Search class: FHUPM-FFSF22-MFFFFFNN
% 2.29/0.77 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.29/0.77 % Starting SubtermCWHack with 31s (1) cores
% 2.29/0.77 % Preprocessing time : 0.001 s
% 2.29/0.77
% 2.29/0.77 % Proof found!
% 2.29/0.77 % SZS status Unsatisfiable
% 2.29/0.77 % SZS output start CNFRefutation
% See solution above
% 2.29/0.77 % Parsed axioms : 15
% 2.29/0.77 % Removed by relevancy pruning/SinE : 4
% 2.29/0.77 % Initial clauses : 11
% 2.29/0.77 % Removed in clause preprocessing : 0
% 2.29/0.77 % Initial clauses in saturation : 11
% 2.29/0.77 % Processed clauses : 1110
% 2.29/0.77 % ...of these trivial : 179
% 2.29/0.77 % ...subsumed : 797
% 2.29/0.77 % ...remaining for further processing : 134
% 2.29/0.77 % Other redundant clauses eliminated : 1300
% 2.29/0.77 % Clauses deleted for lack of memory : 0
% 2.29/0.77 % Backward-subsumed : 2
% 2.29/0.77 % Backward-rewritten : 3
% 2.29/0.77 % Generated clauses : 36345
% 2.29/0.77 % ...of the previous two non-redundant : 19456
% 2.29/0.77 % ...aggressively subsumed : 0
% 2.29/0.77 % Contextual simplify-reflections : 0
% 2.29/0.77 % Paramodulations : 35042
% 2.29/0.77 % Factorizations : 0
% 2.29/0.77 % NegExts : 0
% 2.29/0.77 % Equation resolutions : 1303
% 2.29/0.77 % Disequality decompositions : 0
% 2.29/0.77 % Total rewrite steps : 44988
% 2.29/0.77 % ...of those cached : 38941
% 2.29/0.77 % Propositional unsat checks : 0
% 2.29/0.77 % Propositional check models : 0
% 2.29/0.77 % Propositional check unsatisfiable : 0
% 2.29/0.77 % Propositional clauses : 0
% 2.29/0.77 % Propositional clauses after purity: 0
% 2.29/0.77 % Propositional unsat core size : 0
% 2.29/0.77 % Propositional preprocessing time : 0.000
% 2.29/0.77 % Propositional encoding time : 0.000
% 2.29/0.77 % Propositional solver time : 0.000
% 2.29/0.77 % Success case prop preproc time : 0.000
% 2.29/0.77 % Success case prop encoding time : 0.000
% 2.29/0.77 % Success case prop solver time : 0.000
% 2.29/0.77 % Current number of processed clauses : 129
% 2.29/0.77 % Positive orientable unit clauses : 64
% 2.29/0.77 % Positive unorientable unit clauses: 7
% 2.29/0.77 % Negative unit clauses : 5
% 2.29/0.77 % Non-unit-clauses : 53
% 2.29/0.77 % Current number of unprocessed clauses: 18333
% 2.29/0.77 % ...number of literals in the above : 28009
% 2.29/0.77 % Current number of archived formulas : 0
% 2.29/0.77 % Current number of archived clauses : 5
% 2.29/0.77 % Clause-clause subsumption calls (NU) : 6207
% 2.29/0.77 % Rec. Clause-clause subsumption calls : 6207
% 2.29/0.77 % Non-unit clause-clause subsumptions : 723
% 2.29/0.77 % Unit Clause-clause subsumption calls : 70
% 2.29/0.77 % Rewrite failures with RHS unbound : 0
% 2.29/0.77 % BW rewrite match attempts : 1235
% 2.29/0.77 % BW rewrite match successes : 167
% 2.29/0.77 % Condensation attempts : 0
% 2.29/0.77 % Condensation successes : 0
% 2.29/0.77 % Termbank termtop insertions : 375927
% 2.29/0.77 % Search garbage collected termcells : 19
% 2.29/0.77
% 2.29/0.77 % -------------------------------------------------
% 2.29/0.77 % User time : 0.318 s
% 2.29/0.77 % System time : 0.022 s
% 2.29/0.77 % Total time : 0.340 s
% 2.29/0.77 % Maximum resident set size: 3640 pages
% 2.29/0.77
% 2.29/0.77 % -------------------------------------------------
% 2.29/0.77 % User time : 0.323 s
% 2.29/0.77 % System time : 0.024 s
% 2.29/0.77 % Total time : 0.347 s
% 2.29/0.77 % Maximum resident set size: 4864 pages
% 2.29/0.77 % E exiting
%------------------------------------------------------------------------------