0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.14 % Command : python3 prover_driver.py --schedule_mode external --schedule fof_schedule --no_cores 8 --problem_version fof /export/starexec/sandbox2/benchmark/theBenchmark.p 120 --prover /export/starexec/sandbox2/solver/bin/res/iproveropt_no_z3 0.13/0.34 % Computer : n029.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 02:22:39 EDT 2022 0.13/0.35 % CPUTime : 1.28/1.58 % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p 1.28/1.58 1.28/1.58 %---------------- iProver v3.6 (pre CASC-J11 2022) ----------------% 1.28/1.58 1.28/1.58 ------ iProver source info 1.28/1.58 1.28/1.58 git: date: 2022-07-26 19:47:37 +0300 1.28/1.58 git: sha1: 69e283425f6c8ae3fb9e67f2058d741e849b12e1 1.28/1.58 git: non_committed_changes: false 1.28/1.58 git: last_make_outside_of_git: false 1.28/1.58 1.28/1.58 ------ Parsing... 1.28/1.58 ------ Clausification by vclausify_rel & Parsing by iProver... 1.28/1.58 1.28/1.58 ------ Preprocessing... sup_sim: 3 sf_s rm: 22 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e 1.28/1.58 1.28/1.58 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e 1.28/1.58 1.28/1.58 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e 1.28/1.58 ------ Proving... 1.28/1.58 ------ Problem Properties 1.28/1.58 1.28/1.58 1.28/1.58 clauses 21 1.28/1.58 conjectures 0 1.28/1.58 EPR 0 1.28/1.58 Horn 21 1.28/1.58 unary 19 1.28/1.58 binary 1 1.28/1.58 lits 24 1.28/1.58 lits eq 6 1.28/1.59 fd_pure 0 1.28/1.59 fd_pseudo 0 1.28/1.59 fd_cond 0 1.28/1.59 fd_pseudo_cond 1 1.28/1.59 AC symbols 0 1.28/1.59 1.28/1.59 ------ Schedule dynamic 5 is on 1.28/1.59 1.28/1.59 ------ no conjectures: strip conj schedule 1.28/1.59 1.28/1.59 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10. 1.28/1.59 1.28/1.59 1.28/1.59 ------ 1.28/1.59 Current options: 1.28/1.59 ------ 1.28/1.59 1.28/1.59 1.28/1.59 1.28/1.59 1.28/1.59 ------ Proving... 1.28/1.59 1.28/1.59 1.28/1.59 % SZS status Theorem for theBenchmark.p 1.28/1.59 1.28/1.59 % SZS output start CNFRefutation for theBenchmark.p 1.28/1.59 1.28/1.59 fof(f20,axiom,( 1.28/1.59 r3 <=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3)))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3)). 1.28/1.59 1.28/1.59 fof(f63,plain,( 1.28/1.59 r3 <=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))), 1.28/1.59 inference(rectify,[],[f20])). 1.28/1.59 1.28/1.59 fof(f71,plain,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) => r3), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f63])). 1.28/1.59 1.28/1.59 fof(f94,plain,( 1.28/1.59 r3 | ? [X0,X1] : ~is_a_theorem(implies(or(X0,X1),or(X1,X0)))), 1.28/1.59 inference(ennf_transformation,[],[f71])). 1.28/1.59 1.28/1.59 fof(f105,plain,( 1.28/1.59 ? [X0,X1] : ~is_a_theorem(implies(or(X0,X1),or(X1,X0))) => ~is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))), 1.28/1.59 introduced(choice_axiom,[])). 1.28/1.59 1.28/1.59 fof(f106,plain,( 1.28/1.59 r3 | ~is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))), 1.28/1.59 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f94,f105])). 1.28/1.59 1.28/1.59 fof(f118,plain,( 1.28/1.59 r3 | ~is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))), 1.28/1.59 inference(cnf_transformation,[],[f106])). 1.28/1.59 1.28/1.59 fof(f53,conjecture,( 1.28/1.59 r3), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3)). 1.28/1.59 1.28/1.59 fof(f54,negated_conjecture,( 1.28/1.59 ~r3), 1.28/1.59 inference(negated_conjecture,[],[f53])). 1.28/1.59 1.28/1.59 fof(f66,plain,( 1.28/1.59 ~r3), 1.28/1.59 inference(flattening,[],[f54])). 1.28/1.59 1.28/1.59 fof(f149,plain,( 1.28/1.59 ~r3), 1.28/1.59 inference(cnf_transformation,[],[f66])). 1.28/1.59 1.28/1.59 fof(f30,axiom,( 1.28/1.59 op_or => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or)). 1.28/1.59 1.28/1.59 fof(f103,plain,( 1.28/1.59 ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) | ~op_or), 1.28/1.59 inference(ennf_transformation,[],[f30])). 1.28/1.59 1.28/1.59 fof(f126,plain,( 1.28/1.59 ( ! [X0,X1] : (or(X0,X1) = not(and(not(X0),not(X1))) | ~op_or) )), 1.28/1.59 inference(cnf_transformation,[],[f103])). 1.28/1.59 1.28/1.59 fof(f38,axiom,( 1.28/1.59 op_or), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or)). 1.28/1.59 1.28/1.59 fof(f134,plain,( 1.28/1.59 op_or), 1.28/1.59 inference(cnf_transformation,[],[f38])). 1.28/1.59 1.28/1.59 fof(f27,axiom,( 1.28/1.59 op_implies_and => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and)). 1.28/1.59 1.28/1.59 fof(f100,plain,( 1.28/1.59 ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) | ~op_implies_and), 1.28/1.59 inference(ennf_transformation,[],[f27])). 1.28/1.59 1.28/1.59 fof(f123,plain,( 1.28/1.59 ( ! [X0,X1] : (implies(X0,X1) = not(and(X0,not(X1))) | ~op_implies_and) )), 1.28/1.59 inference(cnf_transformation,[],[f100])). 1.28/1.59 1.28/1.59 fof(f39,axiom,( 1.28/1.59 op_implies_and), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and)). 1.28/1.59 1.28/1.59 fof(f135,plain,( 1.28/1.59 op_implies_and), 1.28/1.59 inference(cnf_transformation,[],[f39])). 1.28/1.59 1.28/1.59 fof(f2,axiom,( 1.28/1.59 modus_tollens <=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens)). 1.28/1.59 1.28/1.59 fof(f81,plain,( 1.28/1.59 modus_tollens => ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f2])). 1.28/1.59 1.28/1.59 fof(f84,plain,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) | ~modus_tollens), 1.28/1.59 inference(ennf_transformation,[],[f81])). 1.28/1.59 1.28/1.59 fof(f108,plain,( 1.28/1.59 ( ! [X0,X1] : (is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) | ~modus_tollens) )), 1.28/1.59 inference(cnf_transformation,[],[f84])). 1.28/1.59 1.28/1.59 fof(f45,axiom,( 1.28/1.59 modus_tollens), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens)). 1.28/1.59 1.28/1.59 fof(f141,plain,( 1.28/1.59 modus_tollens), 1.28/1.59 inference(cnf_transformation,[],[f45])). 1.28/1.59 1.28/1.59 fof(f28,axiom,( 1.28/1.59 op_implies_or => ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or)). 1.28/1.59 1.28/1.59 fof(f101,plain,( 1.28/1.59 ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) | ~op_implies_or), 1.28/1.59 inference(ennf_transformation,[],[f28])). 1.28/1.59 1.28/1.59 fof(f124,plain,( 1.28/1.59 ( ! [X0,X1] : (implies(X0,X1) = or(not(X0),X1) | ~op_implies_or) )), 1.28/1.59 inference(cnf_transformation,[],[f101])). 1.28/1.59 1.28/1.59 fof(f51,axiom,( 1.28/1.59 op_implies_or), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or)). 1.28/1.59 1.28/1.59 fof(f147,plain,( 1.28/1.59 op_implies_or), 1.28/1.59 inference(cnf_transformation,[],[f51])). 1.28/1.59 1.28/1.59 fof(f5,axiom,( 1.28/1.59 and_3 <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3)). 1.28/1.59 1.28/1.59 fof(f78,plain,( 1.28/1.59 and_3 => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f5])). 1.28/1.59 1.28/1.59 fof(f87,plain,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) | ~and_3), 1.28/1.59 inference(ennf_transformation,[],[f78])). 1.28/1.59 1.28/1.59 fof(f111,plain,( 1.28/1.59 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) | ~and_3) )), 1.28/1.59 inference(cnf_transformation,[],[f87])). 1.28/1.59 1.28/1.59 fof(f40,axiom,( 1.28/1.59 and_3), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3)). 1.28/1.59 1.28/1.59 fof(f136,plain,( 1.28/1.59 and_3), 1.28/1.59 inference(cnf_transformation,[],[f40])). 1.28/1.59 1.28/1.59 fof(f18,axiom,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) <=> implies_2), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2)). 1.28/1.59 1.28/1.59 fof(f72,plain,( 1.28/1.59 implies_2 => ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f18])). 1.28/1.59 1.28/1.59 fof(f93,plain,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) | ~implies_2), 1.28/1.59 inference(ennf_transformation,[],[f72])). 1.28/1.59 1.28/1.59 fof(f117,plain,( 1.28/1.59 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) | ~implies_2) )), 1.28/1.59 inference(cnf_transformation,[],[f93])). 1.28/1.59 1.28/1.59 fof(f33,axiom,( 1.28/1.59 implies_2), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2)). 1.28/1.59 1.28/1.59 fof(f129,plain,( 1.28/1.59 implies_2), 1.28/1.59 inference(cnf_transformation,[],[f33])). 1.28/1.59 1.28/1.59 fof(f24,axiom,( 1.28/1.59 modus_ponens <=> ! [X0,X1] : ((is_a_theorem(implies(X0,X1)) & is_a_theorem(X0)) => is_a_theorem(X1))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens)). 1.28/1.59 1.28/1.59 fof(f69,plain,( 1.28/1.59 modus_ponens => ! [X0,X1] : ((is_a_theorem(implies(X0,X1)) & is_a_theorem(X0)) => is_a_theorem(X1))), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f24])). 1.28/1.59 1.28/1.59 fof(f96,plain,( 1.28/1.59 ! [X0,X1] : (is_a_theorem(X1) | (~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0))) | ~modus_ponens), 1.28/1.59 inference(ennf_transformation,[],[f69])). 1.28/1.59 1.28/1.59 fof(f97,plain,( 1.28/1.59 ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0)) | ~modus_ponens), 1.28/1.59 inference(flattening,[],[f96])). 1.28/1.59 1.28/1.59 fof(f120,plain,( 1.28/1.59 ( ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(implies(X0,X1)) | ~is_a_theorem(X0) | ~modus_ponens) )), 1.28/1.59 inference(cnf_transformation,[],[f97])). 1.28/1.59 1.28/1.59 fof(f41,axiom,( 1.28/1.59 modus_ponens), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens)). 1.28/1.59 1.28/1.59 fof(f137,plain,( 1.28/1.59 modus_ponens), 1.28/1.59 inference(cnf_transformation,[],[f41])). 1.28/1.59 1.28/1.59 fof(f29,axiom,( 1.28/1.59 op_equiv => ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv)). 1.28/1.59 1.28/1.59 fof(f102,plain,( 1.28/1.59 ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) | ~op_equiv), 1.28/1.59 inference(ennf_transformation,[],[f29])). 1.28/1.59 1.28/1.59 fof(f125,plain,( 1.28/1.59 ( ! [X0,X1] : (equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) | ~op_equiv) )), 1.28/1.59 inference(cnf_transformation,[],[f102])). 1.28/1.59 1.28/1.59 fof(f50,axiom,( 1.28/1.59 op_equiv), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv)). 1.28/1.59 1.28/1.59 fof(f146,plain,( 1.28/1.59 op_equiv), 1.28/1.59 inference(cnf_transformation,[],[f50])). 1.28/1.59 1.28/1.59 fof(f31,axiom,( 1.28/1.59 op_and => ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and)). 1.28/1.59 1.28/1.59 fof(f104,plain,( 1.28/1.59 ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) | ~op_and), 1.28/1.59 inference(ennf_transformation,[],[f31])). 1.28/1.59 1.28/1.59 fof(f127,plain,( 1.28/1.59 ( ! [X0,X1] : (and(X0,X1) = not(or(not(X0),not(X1))) | ~op_and) )), 1.28/1.59 inference(cnf_transformation,[],[f104])). 1.28/1.59 1.28/1.59 fof(f52,axiom,( 1.28/1.59 op_and), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and)). 1.28/1.59 1.28/1.59 fof(f148,plain,( 1.28/1.59 op_and), 1.28/1.59 inference(cnf_transformation,[],[f52])). 1.28/1.59 1.28/1.59 fof(f6,axiom,( 1.28/1.59 equivalence_3 <=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3)). 1.28/1.59 1.28/1.59 fof(f77,plain,( 1.28/1.59 equivalence_3 => ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f6])). 1.28/1.59 1.28/1.59 fof(f88,plain,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) | ~equivalence_3), 1.28/1.59 inference(ennf_transformation,[],[f77])). 1.28/1.59 1.28/1.59 fof(f112,plain,( 1.28/1.59 ( ! [X0,X1] : (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) | ~equivalence_3) )), 1.28/1.59 inference(cnf_transformation,[],[f88])). 1.28/1.59 1.28/1.59 fof(f37,axiom,( 1.28/1.59 equivalence_3), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3)). 1.28/1.59 1.28/1.59 fof(f133,plain,( 1.28/1.59 equivalence_3), 1.28/1.59 inference(cnf_transformation,[],[f37])). 1.28/1.59 1.28/1.59 fof(f25,axiom,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) <=> implies_1), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1)). 1.28/1.59 1.28/1.59 fof(f68,plain,( 1.28/1.59 implies_1 => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f25])). 1.28/1.59 1.28/1.59 fof(f98,plain,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) | ~implies_1), 1.28/1.59 inference(ennf_transformation,[],[f68])). 1.28/1.59 1.28/1.59 fof(f121,plain,( 1.28/1.59 ( ! [X0,X1] : (is_a_theorem(implies(X0,implies(X1,X0))) | ~implies_1) )), 1.28/1.59 inference(cnf_transformation,[],[f98])). 1.28/1.59 1.28/1.59 fof(f48,axiom,( 1.28/1.59 implies_1), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1)). 1.28/1.59 1.28/1.59 fof(f144,plain,( 1.28/1.59 implies_1), 1.28/1.59 inference(cnf_transformation,[],[f48])). 1.28/1.59 1.28/1.59 fof(f9,axiom,( 1.28/1.59 or_1 <=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1)). 1.28/1.59 1.28/1.59 fof(f76,plain,( 1.28/1.59 or_1 => ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f9])). 1.28/1.59 1.28/1.59 fof(f89,plain,( 1.28/1.59 ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) | ~or_1), 1.28/1.59 inference(ennf_transformation,[],[f76])). 1.28/1.59 1.28/1.59 fof(f113,plain,( 1.28/1.59 ( ! [X0,X1] : (is_a_theorem(implies(X0,or(X0,X1))) | ~or_1) )), 1.28/1.59 inference(cnf_transformation,[],[f89])). 1.28/1.59 1.28/1.59 fof(f36,axiom,( 1.28/1.59 or_1), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1)). 1.28/1.59 1.28/1.59 fof(f132,plain,( 1.28/1.59 or_1), 1.28/1.59 inference(cnf_transformation,[],[f36])). 1.28/1.59 1.28/1.59 fof(f13,axiom,( 1.28/1.59 substitution_of_equivalents <=> ! [X0,X1] : (is_a_theorem(equiv(X0,X1)) => X0 = X1)), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents)). 1.28/1.59 1.28/1.59 fof(f74,plain,( 1.28/1.59 substitution_of_equivalents => ! [X0,X1] : (is_a_theorem(equiv(X0,X1)) => X0 = X1)), 1.28/1.59 inference(unused_predicate_definition_removal,[],[f13])). 1.28/1.59 1.28/1.59 fof(f91,plain,( 1.28/1.59 ! [X0,X1] : (X0 = X1 | ~is_a_theorem(equiv(X0,X1))) | ~substitution_of_equivalents), 1.28/1.59 inference(ennf_transformation,[],[f74])). 1.28/1.59 1.28/1.59 fof(f115,plain,( 1.28/1.59 ( ! [X0,X1] : (X0 = X1 | ~is_a_theorem(equiv(X0,X1)) | ~substitution_of_equivalents) )), 1.28/1.59 inference(cnf_transformation,[],[f91])). 1.28/1.59 1.28/1.59 fof(f49,axiom,( 1.28/1.59 substitution_of_equivalents), 1.28/1.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents)). 1.28/1.59 1.28/1.59 fof(f145,plain,( 1.28/1.59 substitution_of_equivalents), 1.28/1.59 inference(cnf_transformation,[],[f49])). 1.28/1.59 1.28/1.59 cnf(c_60,plain, 1.28/1.59 ( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) | r3 ), 1.28/1.59 inference(cnf_transformation,[],[f118]) ). 1.28/1.59 1.28/1.59 cnf(c_91,negated_conjecture, 1.28/1.59 ( ~ r3 ), 1.28/1.59 inference(cnf_transformation,[],[f149]) ). 1.28/1.59 1.28/1.59 cnf(c_137,plain, 1.28/1.59 ( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_60,c_91]) ). 1.28/1.59 1.28/1.59 cnf(c_68,plain, 1.28/1.59 ( ~ op_or | not(and(not(X0),not(X1))) = or(X0,X1) ), 1.28/1.59 inference(cnf_transformation,[],[f126]) ). 1.28/1.59 1.28/1.59 cnf(c_76,plain,( op_or ),inference(cnf_transformation,[],[f134]) ). 1.28/1.59 1.28/1.59 cnf(c_114,plain, 1.28/1.59 ( not(and(not(X0),not(X1))) = or(X0,X1) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_68,c_76]) ). 1.28/1.59 1.28/1.59 cnf(c_65,plain, 1.28/1.59 ( ~ op_implies_and | not(and(X0,not(X1))) = implies(X0,X1) ), 1.28/1.59 inference(cnf_transformation,[],[f123]) ). 1.28/1.59 1.28/1.59 cnf(c_77,plain,( op_implies_and ),inference(cnf_transformation,[],[f135]) ). 1.28/1.59 1.28/1.59 cnf(c_123,plain, 1.28/1.59 ( not(and(X0,not(X1))) = implies(X0,X1) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_65,c_77]) ). 1.28/1.59 1.28/1.59 cnf(c_267,plain, 1.28/1.59 ( implies(not(X0),X1) = or(X0,X1) ), 1.28/1.59 inference(demodulation,[status(thm)],[c_114,c_123]) ). 1.28/1.59 1.28/1.59 cnf(c_50,plain, 1.28/1.59 ( ~ modus_tollens 1.28/1.59 | is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ), 1.28/1.59 inference(cnf_transformation,[],[f108]) ). 1.28/1.59 1.28/1.59 cnf(c_83,plain,( modus_tollens ),inference(cnf_transformation,[],[f141]) ). 1.28/1.59 1.28/1.59 cnf(c_164,plain, 1.28/1.59 ( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_50,c_83]) ). 1.28/1.59 1.28/1.59 cnf(c_268,plain, 1.28/1.59 ( is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))) ), 1.28/1.59 inference(demodulation,[status(thm)],[c_164,c_267]) ). 1.28/1.59 1.28/1.59 cnf(c_576,plain, 1.28/1.59 ( is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_267,c_268]) ). 1.28/1.59 1.28/1.59 cnf(c_66,plain, 1.28/1.59 ( ~ op_implies_or | or(not(X0),X1) = implies(X0,X1) ), 1.28/1.59 inference(cnf_transformation,[],[f124]) ). 1.28/1.59 1.28/1.59 cnf(c_89,plain,( op_implies_or ),inference(cnf_transformation,[],[f147]) ). 1.28/1.59 1.28/1.59 cnf(c_120,plain, 1.28/1.59 ( or(not(X0),X1) = implies(X0,X1) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_66,c_89]) ). 1.28/1.59 1.28/1.59 cnf(c_53,plain, 1.28/1.59 ( ~ and_3 | is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ), 1.28/1.59 inference(cnf_transformation,[],[f111]) ). 1.28/1.59 1.28/1.59 cnf(c_78,plain,( and_3 ),inference(cnf_transformation,[],[f136]) ). 1.28/1.59 1.28/1.59 cnf(c_155,plain, 1.28/1.59 ( is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_53,c_78]) ). 1.28/1.59 1.28/1.59 cnf(c_542,plain, 1.28/1.59 ( is_a_theorem(implies(X0,or(X1,and(X0,not(X1))))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_267,c_155]) ). 1.28/1.59 1.28/1.59 cnf(c_584,plain, 1.28/1.59 ( is_a_theorem(implies(X0,implies(X1,and(X0,not(not(X1)))))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_120,c_542]) ). 1.28/1.59 1.28/1.59 cnf(c_59,plain, 1.28/1.59 ( ~ implies_2 1.28/1.59 | is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ), 1.28/1.59 inference(cnf_transformation,[],[f117]) ). 1.28/1.59 1.28/1.59 cnf(c_71,plain,( implies_2 ),inference(cnf_transformation,[],[f129]) ). 1.28/1.59 1.28/1.59 cnf(c_139,plain, 1.28/1.59 ( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_59,c_71]) ). 1.28/1.59 1.28/1.59 cnf(c_62,plain, 1.28/1.59 ( ~ is_a_theorem(implies(X0,X1)) 1.28/1.59 | ~ is_a_theorem(X0) 1.28/1.59 | ~ modus_ponens 1.28/1.59 | is_a_theorem(X1) ), 1.28/1.59 inference(cnf_transformation,[],[f120]) ). 1.28/1.59 1.28/1.59 cnf(c_79,plain,( modus_ponens ),inference(cnf_transformation,[],[f137]) ). 1.28/1.59 1.28/1.59 cnf(c_132,plain, 1.28/1.59 ( ~ is_a_theorem(X0) 1.28/1.59 | ~ is_a_theorem(implies(X0,X1)) 1.28/1.59 | is_a_theorem(X1) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_62,c_79]) ). 1.28/1.59 1.28/1.59 cnf(c_133,plain, 1.28/1.59 ( ~ is_a_theorem(implies(X0,X1)) 1.28/1.59 | ~ is_a_theorem(X0) 1.28/1.59 | is_a_theorem(X1) ), 1.28/1.59 inference(renaming,[status(thm)],[c_132]) ). 1.28/1.59 1.28/1.59 cnf(c_728,plain, 1.28/1.59 ( ~ is_a_theorem(implies(X0,implies(X0,X1))) 1.28/1.59 | is_a_theorem(implies(X0,X1)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_139,c_133]) ). 1.28/1.59 1.28/1.59 cnf(c_2281,plain, 1.28/1.59 ( is_a_theorem(implies(X0,and(X0,not(not(X0))))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_584,c_728]) ). 1.28/1.59 1.28/1.59 cnf(c_2609,plain, 1.28/1.59 ( is_a_theorem(or(X0,and(not(X0),not(not(not(X0)))))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_267,c_2281]) ). 1.28/1.59 1.28/1.59 cnf(c_67,plain, 1.28/1.59 ( ~ op_equiv | and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ), 1.28/1.59 inference(cnf_transformation,[],[f125]) ). 1.28/1.59 1.28/1.59 cnf(c_88,plain,( op_equiv ),inference(cnf_transformation,[],[f146]) ). 1.28/1.59 1.28/1.59 cnf(c_117,plain, 1.28/1.59 ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_67,c_88]) ). 1.28/1.59 1.28/1.59 cnf(c_537,plain, 1.28/1.59 ( and(or(X0,X1),implies(X1,not(X0))) = equiv(not(X0),X1) ), 1.28/1.59 inference(superposition,[status(thm)],[c_267,c_117]) ). 1.28/1.59 1.28/1.59 cnf(c_69,plain, 1.28/1.59 ( ~ op_and | not(or(not(X0),not(X1))) = and(X0,X1) ), 1.28/1.59 inference(cnf_transformation,[],[f127]) ). 1.28/1.59 1.28/1.59 cnf(c_90,plain,( op_and ),inference(cnf_transformation,[],[f148]) ). 1.28/1.59 1.28/1.59 cnf(c_111,plain, 1.28/1.59 ( not(or(not(X0),not(X1))) = and(X0,X1) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_69,c_90]) ). 1.28/1.59 1.28/1.59 cnf(c_269,plain, 1.28/1.59 ( not(implies(X0,not(X1))) = and(X0,X1) ), 1.28/1.59 inference(demodulation,[status(thm)],[c_111,c_120]) ). 1.28/1.59 1.28/1.59 cnf(c_631,plain, 1.28/1.59 ( and(X0,implies(X1,not(X2))) = not(implies(X0,and(X1,X2))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_269,c_269]) ). 1.28/1.59 1.28/1.59 cnf(c_890,plain, 1.28/1.59 ( not(implies(or(X0,X1),and(X1,X0))) = equiv(not(X0),X1) ), 1.28/1.59 inference(demodulation,[status(thm)],[c_537,c_631]) ). 1.28/1.59 1.28/1.59 cnf(c_891,plain, 1.28/1.59 ( not(implies(implies(X0,X1),and(X1,not(X0)))) = equiv(not(not(X0)),X1) ), 1.28/1.59 inference(superposition,[status(thm)],[c_120,c_890]) ). 1.28/1.59 1.28/1.59 cnf(c_590,plain, 1.28/1.59 ( implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_123,c_123]) ). 1.28/1.59 1.28/1.59 cnf(c_1633,plain, 1.28/1.59 ( implies(implies(X0,X1),and(X1,not(X0))) = not(equiv(X0,X1)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_117,c_590]) ). 1.28/1.59 1.28/1.59 cnf(c_7272,plain, 1.28/1.59 ( not(not(equiv(X0,X1))) = equiv(not(not(X0)),X1) ), 1.28/1.59 inference(light_normalisation,[status(thm)],[c_891,c_1633]) ). 1.28/1.59 1.28/1.59 cnf(c_54,plain, 1.28/1.59 ( ~ equivalence_3 1.28/1.59 | is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ), 1.28/1.59 inference(cnf_transformation,[],[f112]) ). 1.28/1.59 1.28/1.59 cnf(c_75,plain,( equivalence_3 ),inference(cnf_transformation,[],[f133]) ). 1.28/1.59 1.28/1.59 cnf(c_152,plain, 1.28/1.59 ( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_54,c_75]) ). 1.28/1.59 1.28/1.59 cnf(c_2276,plain, 1.28/1.59 ( is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_152,c_728]) ). 1.28/1.59 1.28/1.59 cnf(c_2450,plain, 1.28/1.59 ( ~ is_a_theorem(implies(X0,X0)) | is_a_theorem(equiv(X0,X0)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_2276,c_133]) ). 1.28/1.59 1.28/1.59 cnf(c_63,plain, 1.28/1.59 ( ~ implies_1 | is_a_theorem(implies(X0,implies(X1,X0))) ), 1.28/1.59 inference(cnf_transformation,[],[f121]) ). 1.28/1.59 1.28/1.59 cnf(c_86,plain,( implies_1 ),inference(cnf_transformation,[],[f144]) ). 1.28/1.59 1.28/1.59 cnf(c_129,plain, 1.28/1.59 ( is_a_theorem(implies(X0,implies(X1,X0))) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_63,c_86]) ). 1.28/1.59 1.28/1.59 cnf(c_2278,plain, 1.28/1.59 ( is_a_theorem(implies(X0,X0)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_129,c_728]) ). 1.28/1.59 1.28/1.59 cnf(c_2451,plain, 1.28/1.59 ( is_a_theorem(equiv(X0,X0)) ), 1.28/1.59 inference(forward_subsumption_resolution,[status(thm)],[c_2450,c_2278]) ). 1.28/1.59 1.28/1.59 cnf(c_7307,plain, 1.28/1.59 ( is_a_theorem(not(not(equiv(X0,not(not(X0)))))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_7272,c_2451]) ). 1.28/1.59 1.28/1.59 cnf(c_55,plain, 1.28/1.59 ( ~ or_1 | is_a_theorem(implies(X0,or(X0,X1))) ), 1.28/1.59 inference(cnf_transformation,[],[f113]) ). 1.28/1.59 1.28/1.59 cnf(c_74,plain,( or_1 ),inference(cnf_transformation,[],[f132]) ). 1.28/1.59 1.28/1.59 cnf(c_150,plain, 1.28/1.59 ( is_a_theorem(implies(X0,or(X0,X1))) ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_55,c_74]) ). 1.28/1.59 1.28/1.59 cnf(c_725,plain, 1.28/1.59 ( ~ is_a_theorem(X0) | is_a_theorem(or(X0,X1)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_150,c_133]) ). 1.28/1.59 1.28/1.59 cnf(c_859,plain, 1.28/1.59 ( ~ is_a_theorem(not(X0)) | is_a_theorem(implies(X0,X1)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_120,c_725]) ). 1.28/1.59 1.28/1.59 cnf(c_881,plain, 1.28/1.59 ( ~ is_a_theorem(not(not(X0))) | is_a_theorem(or(X0,X1)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_267,c_859]) ). 1.28/1.59 1.28/1.59 cnf(c_7514,plain, 1.28/1.59 ( is_a_theorem(or(equiv(X0,not(not(X0))),X1)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_7307,c_881]) ). 1.28/1.59 1.28/1.59 cnf(c_732,plain, 1.28/1.59 ( ~ is_a_theorem(or(X0,not(X1))) | is_a_theorem(implies(X1,X0)) ), 1.28/1.59 inference(superposition,[status(thm)],[c_268,c_133]) ). 1.28/1.59 1.28/1.59 cnf(c_7534,plain, 1.28/1.59 ( is_a_theorem(implies(X0,equiv(X1,not(not(X1))))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_7514,c_732]) ). 1.28/1.59 1.28/1.59 cnf(c_7589,plain, 1.28/1.59 ( ~ is_a_theorem(X0) | is_a_theorem(equiv(X1,not(not(X1)))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_7534,c_133]) ). 1.28/1.59 1.28/1.59 cnf(c_7695,plain, 1.28/1.59 ( is_a_theorem(equiv(X0,not(not(X0)))) ), 1.28/1.59 inference(superposition,[status(thm)],[c_2609,c_7589]) ). 1.28/1.59 1.28/1.59 cnf(c_57,plain, 1.28/1.59 ( ~ is_a_theorem(equiv(X0,X1)) 1.28/1.59 | ~ substitution_of_equivalents 1.28/1.59 | X0 = X1 ), 1.28/1.59 inference(cnf_transformation,[],[f115]) ). 1.28/1.59 1.28/1.59 cnf(c_87,plain, 1.28/1.59 ( substitution_of_equivalents ), 1.28/1.59 inference(cnf_transformation,[],[f145]) ). 1.28/1.59 1.28/1.59 cnf(c_145,plain, 1.28/1.59 ( ~ is_a_theorem(equiv(X0,X1)) | X0 = X1 ), 1.28/1.59 inference(global_propositional_subsumption,[status(thm)],[c_57,c_87]) ). 1.28/1.59 1.28/1.59 cnf(c_7746,plain, 1.28/1.59 ( not(not(X0)) = X0 ), 1.28/1.59 inference(superposition,[status(thm)],[c_7695,c_145]) ). 1.28/1.59 1.28/1.59 cnf(c_7802,plain, 1.28/1.59 ( is_a_theorem(implies(or(X0,X1),or(X1,X0))) ), 1.28/1.59 inference(demodulation,[status(thm)],[c_576,c_7746]) ). 1.28/1.59 1.28/1.59 cnf(c_7807,plain, 1.28/1.59 ( $false ), 1.28/1.59 inference(backward_subsumption_resolution,[status(thm)],[c_137,c_7802]) ). 1.28/1.59 1.28/1.59 1.28/1.59 % SZS output end CNFRefutation for theBenchmark.p 1.28/1.59 1.28/1.59 ------ Statistics 1.28/1.59 1.28/1.59 ------ Selected 1.28/1.59 1.28/1.59 total_time: 0.372 1.28/1.59 1.28/1.60 EOF