%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU083+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 15:01:00 EDT 2024 % Result : Theorem 0.59s 0.67s % Output : CNFRefutation 0.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU083+1 : TPTP v8.2.0. Released v3.2.0. % 0.04/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n018.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 : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Jun 21 13:02:53 EDT 2024 % 0.13/0.34 % CPUTime : % 0.47/0.61 start to proof:theBenchmark % 0.59/0.65 %------------------------------------------- % 0.59/0.65 % File :CSE---1.7 % 0.59/0.65 % Problem :theBenchmark % 0.59/0.65 % Transform :cnf % 0.59/0.65 % Format :tptp:raw % 0.59/0.65 % Command :java -jar mcs_scs.jar %d %s % 0.59/0.65 % 0.59/0.65 % Result :Theorem 0.000000s % 0.59/0.65 % Output :CNFRefutation 0.000000s % 0.59/0.65 %------------------------------------------- % 0.59/0.66 %------------------------------------------------------------------------------ % 0.59/0.66 % File : SEU083+1 : TPTP v8.2.0. Released v3.2.0. % 0.59/0.66 % Domain : Set theory % 0.59/0.66 % Problem : Finite sets, theorem 14 % 0.59/0.66 % Version : [Urb06] axioms : Especial. % 0.59/0.66 % English : % 0.59/0.66 % 0.59/0.66 % Refs : [Dar90] Darmochwal (1990), Finite Sets % 0.59/0.66 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.59/0.66 % Source : [Urb06] % 0.59/0.66 % Names : finset_1__t14_finset_1 [Urb06] % 0.59/0.66 % 0.59/0.66 % Status : Theorem % 0.59/0.66 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.00 v4.0.1, 0.04 v3.7.0, 0.00 v3.2.0 % 0.59/0.66 % Syntax : Number of formulae : 62 ( 10 unt; 0 def) % 0.59/0.66 % Number of atoms : 188 ( 5 equ) % 0.59/0.66 % Maximal formula atoms : 10 ( 3 avg) % 0.59/0.66 % Number of connectives : 147 ( 21 ~; 1 |; 97 &) % 0.59/0.66 % ( 1 <=>; 27 =>; 0 <=; 0 <~>) % 0.59/0.66 % Maximal formula depth : 12 ( 5 avg) % 0.59/0.66 % Maximal term depth : 2 ( 1 avg) % 0.59/0.66 % Number of predicates : 19 ( 18 usr; 0 prp; 1-2 aty) % 0.59/0.66 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty) % 0.59/0.66 % Number of variables : 83 ( 57 !; 26 ?) % 0.59/0.66 % SPC : FOF_THM_RFO_SEQ % 0.59/0.66 % 0.59/0.66 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.59/0.66 % library, www.mizar.org % 0.59/0.66 %------------------------------------------------------------------------------ % 0.59/0.66 fof(reflexivity_r1_tarski,axiom, % 0.59/0.66 ! [A,B] : subset(A,A) ). % 0.59/0.66 % 0.59/0.66 fof(antisymmetry_r2_hidden,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( in(A,B) % 0.59/0.66 => ~ in(B,A) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc4_relat_1,axiom, % 0.59/0.66 ( empty(empty_set) % 0.59/0.66 & relation(empty_set) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc12_relat_1,axiom, % 0.59/0.66 ( empty(empty_set) % 0.59/0.66 & relation(empty_set) % 0.59/0.66 & relation_empty_yielding(empty_set) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc2_ordinal1,axiom, % 0.59/0.66 ( relation(empty_set) % 0.59/0.66 & relation_empty_yielding(empty_set) % 0.59/0.66 & function(empty_set) % 0.59/0.66 & one_to_one(empty_set) % 0.59/0.66 & empty(empty_set) % 0.59/0.66 & epsilon_transitive(empty_set) % 0.59/0.66 & epsilon_connected(empty_set) % 0.59/0.66 & ordinal(empty_set) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc1_xboole_0,axiom, % 0.59/0.66 empty(empty_set) ). % 0.59/0.66 % 0.59/0.66 fof(t1_boole,axiom, % 0.59/0.66 ! [A] : set_union2(A,empty_set) = A ). % 0.59/0.66 % 0.59/0.66 fof(t1_subset,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( in(A,B) % 0.59/0.66 => element(A,B) ) ). % 0.59/0.66 % 0.59/0.66 fof(t4_subset,axiom, % 0.59/0.66 ! [A,B,C] : % 0.59/0.66 ( ( in(A,B) % 0.59/0.66 & element(B,powerset(C)) ) % 0.59/0.66 => element(A,C) ) ). % 0.59/0.66 % 0.59/0.66 fof(t5_subset,axiom, % 0.59/0.66 ! [A,B,C] : % 0.59/0.66 ~ ( in(A,B) % 0.59/0.66 & element(B,powerset(C)) % 0.59/0.66 & empty(C) ) ). % 0.59/0.66 % 0.59/0.66 fof(existence_m1_subset_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ? [B] : element(B,A) ). % 0.59/0.66 % 0.59/0.66 fof(cc1_finset_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( empty(A) % 0.59/0.66 => finite(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc2_finset_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( finite(A) % 0.59/0.66 => ! [B] : % 0.59/0.66 ( element(B,powerset(A)) % 0.59/0.66 => finite(B) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc1_funct_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( empty(A) % 0.59/0.66 => function(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc2_funct_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( ( relation(A) % 0.59/0.66 & empty(A) % 0.59/0.66 & function(A) ) % 0.59/0.66 => ( relation(A) % 0.59/0.66 & function(A) % 0.59/0.66 & one_to_one(A) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc2_relat_1,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( ( relation(A) % 0.59/0.66 & relation(B) ) % 0.59/0.66 => relation(set_union2(A,B)) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc1_relat_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( empty(A) % 0.59/0.66 => relation(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc8_arytm_3,axiom, % 0.59/0.66 ~ empty(positive_rationals) ). % 0.59/0.66 % 0.59/0.66 fof(cc1_arytm_3,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( ordinal(A) % 0.59/0.66 => ! [B] : % 0.59/0.66 ( element(B,A) % 0.59/0.66 => ( epsilon_transitive(B) % 0.59/0.66 & epsilon_connected(B) % 0.59/0.66 & ordinal(B) ) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc2_arytm_3,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( ( empty(A) % 0.59/0.66 & ordinal(A) ) % 0.59/0.66 => ( epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) % 0.59/0.66 & natural(A) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc4_arytm_3,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( element(A,positive_rationals) % 0.59/0.66 => ( ordinal(A) % 0.59/0.66 => ( epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) % 0.59/0.66 & natural(A) ) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc1_ordinal1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( ordinal(A) % 0.59/0.66 => ( epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc2_ordinal1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( ( epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) ) % 0.59/0.66 => ordinal(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(cc3_ordinal1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( empty(A) % 0.59/0.66 => ( epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc1_subset_1,axiom, % 0.59/0.66 ! [A] : ~ empty(powerset(A)) ). % 0.59/0.66 % 0.59/0.66 fof(fc2_xboole_0,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( ~ empty(A) % 0.59/0.66 => ~ empty(set_union2(A,B)) ) ). % 0.59/0.66 % 0.59/0.66 fof(fc3_xboole_0,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( ~ empty(A) % 0.59/0.66 => ~ empty(set_union2(B,A)) ) ). % 0.59/0.66 % 0.59/0.66 fof(t2_subset,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( element(A,B) % 0.59/0.66 => ( empty(B) % 0.59/0.66 | in(A,B) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(t3_subset,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( element(A,powerset(B)) % 0.59/0.66 <=> subset(A,B) ) ). % 0.59/0.66 % 0.59/0.66 fof(t6_boole,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( empty(A) % 0.59/0.66 => A = empty_set ) ). % 0.59/0.66 % 0.59/0.66 fof(t7_boole,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ~ ( in(A,B) % 0.59/0.66 & empty(B) ) ). % 0.59/0.66 % 0.59/0.66 fof(t8_boole,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ~ ( empty(A) % 0.59/0.66 & A != B % 0.59/0.66 & empty(B) ) ). % 0.59/0.66 % 0.59/0.66 fof(commutativity_k2_xboole_0,axiom, % 0.59/0.66 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.59/0.66 % 0.59/0.66 fof(idempotence_k2_xboole_0,axiom, % 0.59/0.66 ! [A,B] : set_union2(A,A) = A ). % 0.59/0.66 % 0.59/0.66 fof(fc9_finset_1,axiom, % 0.59/0.66 ! [A,B] : % 0.59/0.66 ( ( finite(A) % 0.59/0.66 & finite(B) ) % 0.59/0.66 => finite(set_union2(A,B)) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc1_finset_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( ~ empty(A) % 0.59/0.66 & finite(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc2_finset_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ? [B] : % 0.59/0.66 ( element(B,powerset(A)) % 0.59/0.66 & empty(B) % 0.59/0.66 & relation(B) % 0.59/0.66 & function(B) % 0.59/0.66 & one_to_one(B) % 0.59/0.66 & epsilon_transitive(B) % 0.59/0.66 & epsilon_connected(B) % 0.59/0.66 & ordinal(B) % 0.59/0.66 & natural(B) % 0.59/0.66 & finite(B) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc3_finset_1,axiom, % 0.59/0.66 ! [A] : % 0.59/0.66 ( ~ empty(A) % 0.59/0.66 => ? [B] : % 0.59/0.66 ( element(B,powerset(A)) % 0.59/0.66 & ~ empty(B) % 0.59/0.66 & finite(B) ) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc1_funct_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & function(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc2_funct_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & empty(A) % 0.59/0.66 & function(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc3_funct_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & function(A) % 0.59/0.66 & one_to_one(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc4_funct_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & relation_empty_yielding(A) % 0.59/0.66 & function(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc5_funct_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & relation_non_empty(A) % 0.59/0.66 & function(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc1_ordinal2,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) % 0.59/0.66 & being_limit_ordinal(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc2_ordinal2,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & function(A) % 0.59/0.66 & transfinite_sequence(A) % 0.59/0.66 & ordinal_yielding(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc1_relat_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( empty(A) % 0.59/0.66 & relation(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc2_relat_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( ~ empty(A) % 0.59/0.66 & relation(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc3_relat_1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & relation_empty_yielding(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc1_arytm_3,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( ~ empty(A) % 0.59/0.66 & epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) % 0.59/0.66 & natural(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc2_arytm_3,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( element(A,positive_rationals) % 0.59/0.66 & ~ empty(A) % 0.59/0.66 & epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc3_arytm_3,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( element(A,positive_rationals) % 0.59/0.66 & empty(A) % 0.59/0.66 & epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) % 0.59/0.66 & natural(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc1_ordinal1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) ) ). % 0.59/0.66 % 0.59/0.66 fof(rc2_ordinal1,axiom, % 0.59/0.66 ? [A] : % 0.59/0.66 ( relation(A) % 0.59/0.66 & function(A) % 0.59/0.66 & one_to_one(A) % 0.59/0.66 & empty(A) % 0.59/0.66 & epsilon_transitive(A) % 0.59/0.66 & epsilon_connected(A) % 0.59/0.66 & ordinal(A) ) ). % 0.59/0.67 % 0.59/0.67 fof(rc3_ordinal1,axiom, % 0.59/0.67 ? [A] : % 0.59/0.67 ( ~ empty(A) % 0.59/0.67 & epsilon_transitive(A) % 0.59/0.67 & epsilon_connected(A) % 0.59/0.67 & ordinal(A) ) ). % 0.59/0.67 % 0.59/0.67 fof(rc4_ordinal1,axiom, % 0.59/0.67 ? [A] : % 0.59/0.67 ( relation(A) % 0.59/0.67 & function(A) % 0.59/0.67 & transfinite_sequence(A) ) ). % 0.59/0.67 % 0.59/0.67 fof(rc1_subset_1,axiom, % 0.59/0.67 ! [A] : % 0.59/0.67 ( ~ empty(A) % 0.59/0.67 => ? [B] : % 0.59/0.67 ( element(B,powerset(A)) % 0.59/0.67 & ~ empty(B) ) ) ). % 0.59/0.67 % 0.59/0.67 fof(rc2_subset_1,axiom, % 0.59/0.67 ! [A] : % 0.59/0.67 ? [B] : % 0.59/0.67 ( element(B,powerset(A)) % 0.59/0.67 & empty(B) ) ). % 0.59/0.67 % 0.59/0.67 fof(rc1_xboole_0,axiom, % 0.59/0.67 ? [A] : empty(A) ). % 0.59/0.67 % 0.59/0.67 fof(rc2_xboole_0,axiom, % 0.59/0.67 ? [A] : ~ empty(A) ). % 0.59/0.67 % 0.59/0.67 fof(rc1_funcop_1,axiom, % 0.59/0.67 ? [A] : % 0.59/0.67 ( relation(A) % 0.59/0.67 & function(A) % 0.59/0.67 & function_yielding(A) ) ). % 0.59/0.67 % 0.59/0.67 fof(t14_finset_1,conjecture, % 0.59/0.67 ! [A,B] : % 0.59/0.67 ( ( finite(A) % 0.59/0.67 & finite(B) ) % 0.59/0.67 => finite(set_union2(A,B)) ) ). % 0.59/0.67 % 0.59/0.67 fof(l3_finset_1,axiom, % 0.59/0.67 ! [A,B] : % 0.59/0.67 ( ( finite(A) % 0.59/0.67 & finite(B) ) % 0.59/0.67 => finite(set_union2(A,B)) ) ). % 0.59/0.67 % 0.59/0.67 %------------------------------------------------------------------------------ % 0.59/0.67 %------------------------------------------- % 0.59/0.67 % Proof found % 0.59/0.67 % SZS status Theorem for theBenchmark % 0.59/0.67 % SZS output start Proof % 0.59/0.67 %ClaNum:176(EqnAxiom:32) % 0.59/0.67 %VarNum:140(SingletonVarNum:73) % 0.59/0.67 %MaxLitNum:4 % 0.59/0.67 %MaxfuncDepth:1 % 0.59/0.67 %SharedTerms:106 % 0.59/0.67 %goalClause: 99 100 136 % 0.59/0.67 %singleGoalClaCount:3 % 0.59/0.67 [36]P1(a1) % 0.59/0.67 [37]P1(a2) % 0.59/0.67 [38]P1(a3) % 0.59/0.67 [39]P1(a6) % 0.59/0.67 [40]P1(a11) % 0.59/0.67 [41]P1(a13) % 0.59/0.67 [44]P4(a1) % 0.59/0.67 [45]P4(a19) % 0.59/0.67 [46]P4(a2) % 0.59/0.67 [47]P4(a27) % 0.59/0.67 [48]P4(a28) % 0.59/0.67 [49]P4(a29) % 0.59/0.67 [50]P4(a4) % 0.59/0.67 [51]P4(a3) % 0.59/0.67 [52]P4(a7) % 0.59/0.67 [53]P4(a8) % 0.59/0.67 [54]P4(a11) % 0.59/0.67 [55]P4(a14) % 0.59/0.67 [56]P4(a20) % 0.59/0.67 [58]P15(a1) % 0.59/0.67 [59]P15(a28) % 0.59/0.67 [60]P15(a8) % 0.59/0.67 [61]P5(a1) % 0.59/0.67 [62]P5(a19) % 0.59/0.67 [63]P5(a2) % 0.59/0.67 [64]P5(a27) % 0.59/0.67 [65]P5(a28) % 0.59/0.67 [66]P5(a29) % 0.59/0.67 [67]P5(a4) % 0.59/0.67 [68]P5(a11) % 0.59/0.67 [69]P5(a14) % 0.59/0.67 [70]P5(a20) % 0.59/0.67 [71]P9(a1) % 0.59/0.67 [72]P9(a27) % 0.59/0.67 [73]P9(a11) % 0.59/0.67 [74]P6(a1) % 0.59/0.67 [75]P6(a5) % 0.59/0.67 [76]P6(a9) % 0.59/0.67 [77]P6(a10) % 0.59/0.67 [78]P6(a6) % 0.59/0.67 [79]P6(a12) % 0.59/0.67 [80]P6(a11) % 0.59/0.67 [81]P6(a15) % 0.59/0.67 [82]P7(a1) % 0.59/0.67 [83]P7(a5) % 0.59/0.67 [84]P7(a9) % 0.59/0.67 [85]P7(a10) % 0.59/0.67 [86]P7(a6) % 0.59/0.67 [87]P7(a12) % 0.59/0.67 [88]P7(a11) % 0.59/0.67 [89]P7(a15) % 0.59/0.67 [90]P13(a1) % 0.59/0.67 [91]P13(a5) % 0.59/0.67 [92]P13(a9) % 0.59/0.67 [93]P13(a10) % 0.59/0.67 [94]P13(a6) % 0.59/0.67 [95]P13(a12) % 0.59/0.67 [96]P13(a11) % 0.59/0.67 [97]P13(a15) % 0.59/0.67 [98]P8(a22) % 0.59/0.67 [99]P8(a23) % 0.59/0.67 [100]P8(a24) % 0.59/0.67 [101]P10(a9) % 0.59/0.67 [102]P10(a6) % 0.59/0.67 [103]P16(a29) % 0.59/0.67 [104]P2(a5) % 0.59/0.67 [105]P17(a4) % 0.59/0.67 [106]P17(a14) % 0.59/0.67 [107]P14(a4) % 0.59/0.67 [108]P11(a20) % 0.59/0.67 [119]P3(a10,a30) % 0.59/0.67 [120]P3(a6,a30) % 0.59/0.67 [128]~P1(a30) % 0.59/0.67 [129]~P1(a22) % 0.59/0.67 [130]~P1(a7) % 0.59/0.67 [131]~P1(a9) % 0.59/0.67 [132]~P1(a10) % 0.59/0.67 [133]~P1(a15) % 0.59/0.67 [134]~P1(a21) % 0.59/0.67 [136]~P8(f31(a23,a24)) % 0.59/0.67 [122]P18(x1221,x1221) % 0.59/0.67 [109]P1(f25(x1091)) % 0.59/0.67 [110]P1(f17(x1101)) % 0.59/0.67 [111]P4(f25(x1111)) % 0.59/0.67 [112]P5(f25(x1121)) % 0.59/0.67 [113]P9(f25(x1131)) % 0.59/0.67 [114]P6(f25(x1141)) % 0.59/0.67 [115]P7(f25(x1151)) % 0.59/0.67 [116]P13(f25(x1161)) % 0.59/0.67 [117]P8(f25(x1171)) % 0.59/0.67 [118]P10(f25(x1181)) % 0.59/0.67 [121]E(f31(x1211,a1),x1211) % 0.59/0.67 [123]E(f31(x1231,x1231),x1231) % 0.59/0.67 [124]P3(f16(x1241),x1241) % 0.59/0.67 [125]P3(f25(x1251),f32(x1251)) % 0.59/0.67 [126]P3(f17(x1261),f32(x1261)) % 0.59/0.67 [135]~P1(f32(x1351)) % 0.59/0.67 [127]E(f31(x1271,x1272),f31(x1272,x1271)) % 0.59/0.67 [137]~P1(x1371)+E(x1371,a1) % 0.59/0.67 [138]~P1(x1381)+P4(x1381) % 0.59/0.67 [139]~P1(x1391)+P5(x1391) % 0.59/0.67 [140]~P1(x1401)+P6(x1401) % 0.59/0.67 [141]~P13(x1411)+P6(x1411) % 0.59/0.67 [142]~P1(x1421)+P7(x1421) % 0.59/0.67 [143]~P13(x1431)+P7(x1431) % 0.59/0.67 [144]~P1(x1441)+P13(x1441) % 0.59/0.67 [145]~P1(x1451)+P8(x1451) % 0.59/0.67 [146]P1(x1461)+P8(f26(x1461)) % 0.59/0.67 [152]P1(x1521)+~P1(f26(x1521)) % 0.59/0.67 [153]P1(x1531)+~P1(f18(x1531)) % 0.59/0.67 [156]P1(x1561)+P3(f26(x1561),f32(x1561)) % 0.59/0.67 [157]P1(x1571)+P3(f18(x1571),f32(x1571)) % 0.59/0.67 [155]~P1(x1551)+~P12(x1552,x1551) % 0.59/0.67 [164]~P12(x1641,x1642)+P3(x1641,x1642) % 0.59/0.67 [171]~P12(x1712,x1711)+~P12(x1711,x1712) % 0.59/0.67 [166]~P18(x1661,x1662)+P3(x1661,f32(x1662)) % 0.59/0.67 [172]P18(x1721,x1722)+~P3(x1721,f32(x1722)) % 0.59/0.67 [173]P1(x1731)+~P1(f31(x1732,x1731)) % 0.59/0.67 [174]P1(x1741)+~P1(f31(x1741,x1742)) % 0.59/0.67 [150]~P6(x1501)+~P7(x1501)+P13(x1501) % 0.59/0.67 [151]~P1(x1511)+~P13(x1511)+P10(x1511) % 0.59/0.67 [160]~P13(x1601)+P10(x1601)+~P3(x1601,a30) % 0.59/0.67 [147]~P1(x1472)+~P1(x1471)+E(x1471,x1472) % 0.59/0.67 [161]~P3(x1611,x1612)+P6(x1611)+~P13(x1612) % 0.59/0.67 [162]~P3(x1621,x1622)+P7(x1621)+~P13(x1622) % 0.59/0.67 [163]~P3(x1631,x1632)+P13(x1631)+~P13(x1632) % 0.59/0.67 [165]~P3(x1652,x1651)+P1(x1651)+P12(x1652,x1651) % 0.59/0.67 [167]P8(x1671)+~P8(x1672)+~P3(x1671,f32(x1672)) % 0.59/0.67 [168]~P4(x1682)+~P4(x1681)+P4(f31(x1681,x1682)) % 0.59/0.67 [170]~P8(x1702)+~P8(x1701)+P8(f31(x1701,x1702)) % 0.59/0.67 [175]~P1(x1751)+~P12(x1752,x1753)+~P3(x1753,f32(x1751)) % 0.59/0.67 [176]P3(x1761,x1762)+~P12(x1761,x1763)+~P3(x1763,f32(x1762)) % 0.59/0.67 [154]~P1(x1541)+~P4(x1541)+~P5(x1541)+P9(x1541) % 0.59/0.67 %EqnAxiom % 0.59/0.67 [1]E(x11,x11) % 0.59/0.67 [2]E(x22,x21)+~E(x21,x22) % 0.59/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.59/0.67 [4]~E(x41,x42)+E(f25(x41),f25(x42)) % 0.59/0.67 [5]~E(x51,x52)+E(f17(x51),f17(x52)) % 0.59/0.67 [6]~E(x61,x62)+E(f32(x61),f32(x62)) % 0.59/0.67 [7]~E(x71,x72)+E(f18(x71),f18(x72)) % 0.59/0.67 [8]~E(x81,x82)+E(f31(x81,x83),f31(x82,x83)) % 0.59/0.67 [9]~E(x91,x92)+E(f31(x93,x91),f31(x93,x92)) % 0.59/0.67 [10]~E(x101,x102)+E(f26(x101),f26(x102)) % 0.59/0.67 [11]~E(x111,x112)+E(f16(x111),f16(x112)) % 0.59/0.67 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 0.59/0.67 [13]P3(x132,x133)+~E(x131,x132)+~P3(x131,x133) % 0.59/0.67 [14]P3(x143,x142)+~E(x141,x142)+~P3(x143,x141) % 0.59/0.67 [15]P12(x152,x153)+~E(x151,x152)+~P12(x151,x153) % 0.59/0.67 [16]P12(x163,x162)+~E(x161,x162)+~P12(x163,x161) % 0.59/0.67 [17]~P13(x171)+P13(x172)+~E(x171,x172) % 0.59/0.67 [18]~P7(x181)+P7(x182)+~E(x181,x182) % 0.59/0.67 [19]~P8(x191)+P8(x192)+~E(x191,x192) % 0.59/0.67 [20]~P6(x201)+P6(x202)+~E(x201,x202) % 0.59/0.67 [21]P18(x212,x213)+~E(x211,x212)+~P18(x211,x213) % 0.59/0.67 [22]P18(x223,x222)+~E(x221,x222)+~P18(x223,x221) % 0.59/0.67 [23]~P5(x231)+P5(x232)+~E(x231,x232) % 0.59/0.67 [24]~P4(x241)+P4(x242)+~E(x241,x242) % 0.59/0.67 [25]~P16(x251)+P16(x252)+~E(x251,x252) % 0.59/0.67 [26]~P2(x261)+P2(x262)+~E(x261,x262) % 0.59/0.67 [27]~P17(x271)+P17(x272)+~E(x271,x272) % 0.59/0.67 [28]~P9(x281)+P9(x282)+~E(x281,x282) % 0.59/0.67 [29]~P14(x291)+P14(x292)+~E(x291,x292) % 0.59/0.67 [30]~P11(x301)+P11(x302)+~E(x301,x302) % 0.59/0.67 [31]~P10(x311)+P10(x312)+~E(x311,x312) % 0.59/0.67 [32]~P15(x321)+P15(x322)+~E(x321,x322) % 0.59/0.67 % 0.59/0.67 %------------------------------------------- % 0.59/0.67 cnf(183,plain, % 0.59/0.67 (P3(f16(x1831),x1831)), % 0.59/0.67 inference(rename_variables,[],[124])). % 0.59/0.67 cnf(188,plain, % 0.59/0.67 ($false), % 0.59/0.67 inference(scs_inference,[],[99,100,136,123,124,183,36,145,2,155,172,167,170]), % 0.59/0.67 ['proof']). % 0.59/0.67 % SZS output end Proof % 0.59/0.67 % Total time :0.000000s %------------------------------------------------------------------------------