%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL026-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 01:11:34 PM UTC 2026
% Result : Unsatisfiable 11.08s 2.64s
% Output : CNFRefutation 11.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 4 RR)
% Number of literals : 55 ( 54 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 : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 132 ( 44 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/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(c0_2,axiom,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_2) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c0_6,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_6) ).
cnf(c0_5,axiom,
is_a_theorem(implies(implies(implies(X1,falsehood),falsehood),X1)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_5) ).
cnf(prove_c0_3,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c0_3) ).
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(X1,implies(X2,X1))) = true,
c0_2 ).
cnf(c_0_8,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_9,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X1)),X3)),true,is_a_theorem(X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_10,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))) = true,
c0_6 ).
cnf(c_0_11,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).
cnf(c_0_12,plain,
ifeq(is_a_theorem(X1),true,is_a_theorem(implies(X2,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(X1,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_11]),c_0_8]) ).
cnf(c_0_14,axiom,
is_a_theorem(implies(implies(implies(X1,falsehood),falsehood),X1)) = true,
c0_5 ).
cnf(c_0_15,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_7]),c_0_8]) ).
cnf(c_0_16,plain,
ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_8]) ).
cnf(c_0_17,plain,
ifeq(is_a_theorem(implies(X1,implies(X2,X3))),true,is_a_theorem(implies(implies(X1,X2),implies(X1,X3))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_10]),c_0_8]) ).
cnf(c_0_18,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,falsehood),falsehood),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_14]),c_0_8]) ).
cnf(c_0_19,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,X2))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_15]),c_0_8]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_8]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,falsehood),falsehood)),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8]) ).
cnf(c_0_22,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_8]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(falsehood,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_8]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X2)),X4),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_22]),c_0_8]) ).
cnf(c_0_25,plain,
is_a_theorem(implies(X1,implies(falsehood,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_23]),c_0_8]) ).
cnf(c_0_26,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_10]),c_0_8]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,implies(X3,X2)),X4)),implies(X1,X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_8]) ).
cnf(c_0_28,plain,
is_a_theorem(implies(implies(X1,falsehood),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_8]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,X1),X3)),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_8]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(implies(implies(X1,falsehood),X1),implies(implies(X1,falsehood),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_8]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(implies(X2,X3),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_20]),c_0_8]) ).
cnf(c_0_32,plain,
ifeq(is_a_theorem(implies(X1,implies(implies(X2,X1),X3))),true,is_a_theorem(implies(X1,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_29]),c_0_8]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,falsehood),X2),implies(implies(X2,falsehood),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_30]),c_0_8]) ).
cnf(c_0_34,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(implies(implies(X2,X3),X2),implies(implies(X2,X3),X3))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_31]),c_0_8]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(X1,implies(implies(X1,falsehood),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_8]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_8]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(X1,implies(implies(X2,implies(implies(X3,X2),X4)),implies(X2,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_29]),c_0_8]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X2,falsehood),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_35]),c_0_8]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_36]),c_0_8]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_8]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X1),falsehood),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_38]),c_0_8]) ).
cnf(c_0_42,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2)),X3)),true,is_a_theorem(X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_20]),c_0_8]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(implies(X2,X3),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_39]),c_0_8]) ).
cnf(c_0_44,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_40]),c_0_8]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,X1),falsehood)),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_41]),c_0_8]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(implies(implies(X1,falsehood),X1),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_21]),c_0_8]) ).
cnf(c_0_47,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X1,implies(implies(X2,X3),X3))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_43]),c_0_8]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_8]) ).
cnf(c_0_49,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
inference(fof_simplification,[status(thm)],[prove_c0_3]) ).
cnf(c_0_50,plain,
ifeq(is_a_theorem(implies(implies(X1,falsehood),X1)),true,is_a_theorem(X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_46]),c_0_8]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(implies(implies(X2,X3),X4),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_8]) ).
cnf(c_0_52,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
c_0_49 ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_8]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL026-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.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 00:00:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 11.08/2.64 % Version: 3.5.1
% 11.08/2.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 11.08/2.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.08/2.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 11.08/2.64 % Starting new_bool_3 with 300s (1) cores
% 11.08/2.64 % Starting new_bool_1 with 300s (1) cores
% 11.08/2.64 % Starting sh5l with 300s (1) cores
% 11.08/2.64 % new_bool_3 with pid 2104432 completed with status 9
% 11.08/2.64 % new_bool_1 with pid 2104433 completed with status 9
% 11.08/2.64 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2104431 completed with status 0
% 11.08/2.64 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 11.08/2.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 11.08/2.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.08/2.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 11.08/2.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.08/2.64 % No SInE strategy applied
% 11.08/2.64 % Search class: FUUPM-FFSF32-MFFFFFNN
% 11.08/2.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.08/2.64 % Starting SubtermCWHack with 136s (1) cores
% 11.08/2.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 11.08/2.64 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 11.08/2.64 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 11.08/2.64 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 11.08/2.64 % G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with pid 2104441 completed with status 0
% 11.08/2.64 % Result found by G-E--_208_B02_F1_AE_CS_SP_PS_S0Y
% 11.08/2.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 11.08/2.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.08/2.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 11.08/2.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.08/2.64 % No SInE strategy applied
% 11.08/2.64 % Search class: FUUPM-FFSF32-MFFFFFNN
% 11.08/2.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.08/2.64 % Starting SubtermCWHack with 136s (1) cores
% 11.08/2.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 11.08/2.64 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 11.08/2.64 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 11.08/2.64 % Preprocessing time : 0.001 s
% 11.08/2.64 % Presaturation interreduction done
% 11.08/2.64
% 11.08/2.64 % Proof found!
% 11.08/2.64 % SZS status Unsatisfiable
% 11.08/2.64 % SZS output start CNFRefutation
% See solution above
% 11.08/2.64 % Parsed axioms : 6
% 11.08/2.64 % Removed by relevancy pruning/SinE : 0
% 11.08/2.64 % Initial clauses : 6
% 11.08/2.64 % Removed in clause preprocessing : 0
% 11.08/2.64 % Initial clauses in saturation : 6
% 11.08/2.64 % Processed clauses : 1482
% 11.08/2.64 % ...of these trivial : 550
% 11.08/2.64 % ...subsumed : 0
% 11.08/2.64 % ...remaining for further processing : 932
% 11.08/2.64 % Other redundant clauses eliminated : 0
% 11.08/2.64 % Clauses deleted for lack of memory : 0
% 11.08/2.64 % Backward-subsumed : 0
% 11.08/2.64 % Backward-rewritten : 32
% 11.08/2.64 % Generated clauses : 155251
% 11.08/2.64 % ...of the previous two non-redundant : 24213
% 11.08/2.64 % ...aggressively subsumed : 0
% 11.08/2.64 % Contextual simplify-reflections : 0
% 11.08/2.64 % Paramodulations : 155251
% 11.08/2.64 % Factorizations : 0
% 11.08/2.64 % NegExts : 0
% 11.08/2.64 % Equation resolutions : 0
% 11.08/2.64 % Disequality decompositions : 0
% 11.08/2.64 % Total rewrite steps : 205170
% 11.08/2.64 % ...of those cached : 114662
% 11.08/2.64 % Propositional unsat checks : 0
% 11.08/2.64 % Propositional check models : 0
% 11.08/2.64 % Propositional check unsatisfiable : 0
% 11.08/2.64 % Propositional clauses : 0
% 11.08/2.64 % Propositional clauses after purity: 0
% 11.08/2.64 % Propositional unsat core size : 0
% 11.08/2.64 % Propositional preprocessing time : 0.000
% 11.08/2.64 % Propositional encoding time : 0.000
% 11.08/2.64 % Propositional solver time : 0.000
% 11.08/2.64 % Success case prop preproc time : 0.000
% 11.08/2.64 % Success case prop encoding time : 0.000
% 11.08/2.64 % Success case prop solver time : 0.000
% 11.08/2.64 % Current number of processed clauses : 894
% 11.08/2.64 % Positive orientable unit clauses : 894
% 11.08/2.64 % Positive unorientable unit clauses: 0
% 11.08/2.64 % Negative unit clauses : 0
% 11.08/2.64 % Non-unit-clauses : 0
% 11.08/2.64 % Current number of unprocessed clauses: 22721
% 11.08/2.64 % ...number of literals in the above : 22721
% 11.08/2.64 % Current number of archived formulas : 0
% 11.08/2.64 % Current number of archived clauses : 38
% 11.08/2.64 % Clause-clause subsumption calls (NU) : 0
% 11.08/2.64 % Rec. Clause-clause subsumption calls : 0
% 11.08/2.64 % Non-unit clause-clause subsumptions : 0
% 11.08/2.64 % Unit Clause-clause subsumption calls : 0
% 11.08/2.64 % Rewrite failures with RHS unbound : 0
% 11.08/2.64 % BW rewrite match attempts : 187090
% 11.08/2.64 % BW rewrite match successes : 32
% 11.08/2.64 % Condensation attempts : 0
% 11.08/2.64 % Condensation successes : 0
% 11.08/2.64 % Termbank termtop insertions : 2702987
% 11.08/2.64 % Search garbage collected termcells : 2
% 11.08/2.64
% 11.08/2.64 % -------------------------------------------------
% 11.08/2.64 % User time : 2.115 s
% 11.08/2.64 % System time : 0.071 s
% 11.08/2.64 % Total time : 2.186 s
% 11.08/2.64 % Maximum resident set size: 3376 pages
% 11.08/2.64
% 11.08/2.64 % -------------------------------------------------
% 11.08/2.64 % User time : 10.710 s
% 11.08/2.64 % System time : 0.337 s
% 11.08/2.64 % Total time : 11.047 s
% 11.08/2.64 % Maximum resident set size: 4608 pages
% 11.08/2.64 % E exiting
%------------------------------------------------------------------------------