%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL050-10 : TPTP v9.3.1. Released v7.3.0.
% 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 01:11:37 PM UTC 2026
% Result : Unsatisfiable 3.05s 1.15s
% Output : CNFRefutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 6
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 4 RR)
% Number of literals : 57 ( 56 equ; 3 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 145 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
cnf(prove_cn_21,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_21) ).
cnf(c_0_6,axiom,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
condensed_detachment ).
cnf(c_0_7,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
cn_1 ).
cnf(c_0_8,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_9,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)) = true,
cn_2 ).
cnf(c_0_10,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(X2,X3),implies(X1,X3))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_11,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))) = true,
cn_3 ).
cnf(c_0_12,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X1),X1),X1),X2)),true,is_a_theorem(X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_8]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_8]) ).
cnf(c_0_14,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(not(X1),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_8]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(X1,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_8]) ).
cnf(c_0_16,plain,
is_a_theorem(implies(not(implies(X1,X1)),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_8]) ).
cnf(c_0_17,plain,
ifeq(is_a_theorem(implies(implies(not(X1),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_8]) ).
cnf(c_0_18,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,X3)),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_16]),c_0_8]) ).
cnf(c_0_19,plain,
is_a_theorem(implies(X1,implies(not(implies(X2,X2)),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X4,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_19]),c_0_8]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(X1,implies(X2,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_20]),c_0_8]) ).
cnf(c_0_22,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_21]),c_0_8]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X4,X4),X2),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_22]),c_0_8]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_23]),c_0_8]) ).
cnf(c_0_25,plain,
ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(implies(X3,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_22]),c_0_8]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,X3),X1),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_8]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_7]),c_0_8]) ).
cnf(c_0_28,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X2),X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_8]) ).
cnf(c_0_29,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X2)),X4)),true,is_a_theorem(implies(implies(X3,X1),X4)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_27]),c_0_8]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X1),X2),X2),X3),implies(X4,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_28]),c_0_8]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,X2),X3)),implies(X4,implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_8]) ).
cnf(c_0_32,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,implies(implies(X2,X4),X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_8]) ).
cnf(c_0_33,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X1),X2),X2),X3)),true,is_a_theorem(X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_24]),c_0_8]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(implies(X1,X2),implies(X3,implies(implies(implies(X1,X2),X4),X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_8]) ).
cnf(c_0_35,plain,
ifeq(is_a_theorem(implies(not(X1),X1)),true,is_a_theorem(X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_8]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(implies(X2,X2),X3),X3),X4),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_8]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X1),X2),X2),X3),X3)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_8]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_8]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,X2),X3)),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_37]),c_0_8]) ).
cnf(c_0_40,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(implies(not(X1),X1),X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_38]),c_0_8]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(implies(X2,X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_39]),c_0_8]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_8]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42]),c_0_8]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_43]),c_0_8]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(X1,implies(implies(X2,X1),X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_44]),c_0_8]) ).
cnf(c_0_46,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X1),X2),X3),implies(X1,X3)),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_8]) ).
cnf(c_0_47,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_45]),c_0_8]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_8]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_48]),c_0_8]) ).
cnf(c_0_50,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_49]),c_0_8]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_8]) ).
cnf(c_0_52,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true,
inference(fof_simplification,[status(thm)],[prove_cn_21]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_51]),c_0_8]) ).
cnf(c_0_54,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true,
c_0_52 ).
cnf(c_0_55,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_53]),c_0_8]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL050-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:02:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.05/1.15 % Version: 3.5.1
% 3.05/1.15 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.05/1.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.05/1.15 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.05/1.15 % Starting new_bool_3 with 300s (1) cores
% 3.05/1.15 % Starting new_bool_1 with 300s (1) cores
% 3.05/1.15 % Starting sh5l with 300s (1) cores
% 3.05/1.15 % new_bool_3 with pid 2108391 completed with status 9
% 3.05/1.15 % new_bool_1 with pid 2108392 completed with status 9
% 3.05/1.15 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2108390 completed with status 0
% 3.05/1.15 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 3.05/1.15 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.05/1.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.05/1.15 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.05/1.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.05/1.15 % No SInE strategy applied
% 3.05/1.15 % Search class: FUUPM-FFSF32-MFFFFFNN
% 3.05/1.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.05/1.15 % Starting SubtermCWHack with 136s (1) cores
% 3.05/1.15 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 3.05/1.15 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 3.05/1.15 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 3.05/1.15 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 3.05/1.15 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2108396 completed with status 0
% 3.05/1.15 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 3.05/1.15 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.05/1.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.05/1.15 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.05/1.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.05/1.15 % No SInE strategy applied
% 3.05/1.15 % Search class: FUUPM-FFSF32-MFFFFFNN
% 3.05/1.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.05/1.15 % Starting SubtermCWHack with 136s (1) cores
% 3.05/1.15 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 3.05/1.15 % Preprocessing time : 0.007 s
% 3.05/1.15
% 3.05/1.15 % Proof found!
% 3.05/1.15 % SZS status Unsatisfiable
% 3.05/1.15 % SZS output start CNFRefutation
% See solution above
% 3.05/1.15 % Parsed axioms : 6
% 3.05/1.15 % Removed by relevancy pruning/SinE : 0
% 3.05/1.15 % Initial clauses : 6
% 3.05/1.15 % Removed in clause preprocessing : 0
% 3.05/1.15 % Initial clauses in saturation : 6
% 3.05/1.15 % Processed clauses : 682
% 3.05/1.15 % ...of these trivial : 182
% 3.05/1.15 % ...subsumed : 0
% 3.05/1.15 % ...remaining for further processing : 500
% 3.05/1.15 % Other redundant clauses eliminated : 0
% 3.05/1.15 % Clauses deleted for lack of memory : 0
% 3.05/1.15 % Backward-subsumed : 0
% 3.05/1.15 % Backward-rewritten : 24
% 3.05/1.15 % Generated clauses : 59013
% 3.05/1.15 % ...of the previous two non-redundant : 12939
% 3.05/1.15 % ...aggressively subsumed : 0
% 3.05/1.15 % Contextual simplify-reflections : 0
% 3.05/1.15 % Paramodulations : 59013
% 3.05/1.15 % Factorizations : 0
% 3.05/1.15 % NegExts : 0
% 3.05/1.15 % Equation resolutions : 0
% 3.05/1.15 % Disequality decompositions : 0
% 3.05/1.15 % Total rewrite steps : 68498
% 3.05/1.15 % ...of those cached : 37196
% 3.05/1.15 % Propositional unsat checks : 0
% 3.05/1.15 % Propositional check models : 0
% 3.05/1.15 % Propositional check unsatisfiable : 0
% 3.05/1.15 % Propositional clauses : 0
% 3.05/1.15 % Propositional clauses after purity: 0
% 3.05/1.15 % Propositional unsat core size : 0
% 3.05/1.15 % Propositional preprocessing time : 0.000
% 3.05/1.15 % Propositional encoding time : 0.000
% 3.05/1.15 % Propositional solver time : 0.000
% 3.05/1.15 % Success case prop preproc time : 0.000
% 3.05/1.15 % Success case prop encoding time : 0.000
% 3.05/1.15 % Success case prop solver time : 0.000
% 3.05/1.15 % Current number of processed clauses : 476
% 3.05/1.15 % Positive orientable unit clauses : 476
% 3.05/1.15 % Positive unorientable unit clauses: 0
% 3.05/1.15 % Negative unit clauses : 0
% 3.05/1.15 % Non-unit-clauses : 0
% 3.05/1.15 % Current number of unprocessed clauses: 12218
% 3.05/1.15 % ...number of literals in the above : 12218
% 3.05/1.15 % Current number of archived formulas : 0
% 3.05/1.15 % Current number of archived clauses : 24
% 3.05/1.15 % Clause-clause subsumption calls (NU) : 0
% 3.05/1.15 % Rec. Clause-clause subsumption calls : 0
% 3.05/1.15 % Non-unit clause-clause subsumptions : 0
% 3.05/1.15 % Unit Clause-clause subsumption calls : 0
% 3.05/1.15 % Rewrite failures with RHS unbound : 0
% 3.05/1.15 % BW rewrite match attempts : 32130
% 3.05/1.15 % BW rewrite match successes : 24
% 3.05/1.15 % Condensation attempts : 0
% 3.05/1.15 % Condensation successes : 0
% 3.05/1.15 % Termbank termtop insertions : 926977
% 3.05/1.15 % Search garbage collected termcells : 2
% 3.05/1.15
% 3.05/1.15 % -------------------------------------------------
% 3.05/1.15 % User time : 0.682 s
% 3.05/1.15 % System time : 0.034 s
% 3.05/1.15 % Total time : 0.716 s
% 3.05/1.15 % Maximum resident set size: 3632 pages
% 3.05/1.15
% 3.05/1.15 % -------------------------------------------------
% 3.05/1.15 % User time : 3.478 s
% 3.05/1.15 % System time : 0.196 s
% 3.05/1.15 % Total time : 3.674 s
% 3.05/1.15 % Maximum resident set size: 4608 pages
% 3.05/1.15 % E exiting
%------------------------------------------------------------------------------