%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU152+2 : TPTP v8.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n024.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 15:01:22 EDT 2024 % Result : Theorem 0.55s 0.66s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU152+2 : TPTP v8.2.0. Released v3.3.0. % 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Jun 21 14:11:09 EDT 2024 % 0.12/0.34 % CPUTime : % 0.54/0.58 start to proof:theBenchmark % 0.55/0.64 %------------------------------------------- % 0.55/0.64 % File :CSE---1.7 % 0.55/0.64 % Problem :theBenchmark % 0.55/0.64 % Transform :cnf % 0.55/0.64 % Format :tptp:raw % 0.55/0.64 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.64 % 0.55/0.64 % Result :Theorem 0.000000s % 0.55/0.64 % Output :CNFRefutation 0.000000s % 0.55/0.64 %------------------------------------------- % 0.55/0.65 %------------------------------------------------------------------------------ % 0.55/0.65 % File : SEU152+2 : TPTP v8.2.0. Released v3.3.0. % 0.55/0.65 % Domain : Set theory % 0.55/0.65 % Problem : MPTP chainy problem l23_zfmisc_1 % 0.55/0.65 % Version : [Urb07] axioms : Especial. % 0.55/0.65 % English : % 0.55/0.65 % 0.55/0.65 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 0.55/0.65 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 0.55/0.65 % Source : [Urb07] % 0.55/0.65 % Names : chainy-l23_zfmisc_1 [Urb07] % 0.55/0.65 % 0.55/0.65 % Status : Theorem % 0.55/0.65 % Rating : 0.08 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.30 v5.2.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.25 v3.5.0, 0.26 v3.3.0 % 0.55/0.65 % Syntax : Number of formulae : 75 ( 31 unt; 0 def) % 0.55/0.65 % Number of atoms : 147 ( 49 equ) % 0.55/0.65 % Maximal formula atoms : 6 ( 1 avg) % 0.55/0.65 % Number of connectives : 99 ( 27 ~; 4 |; 22 &) % 0.55/0.65 % ( 23 <=>; 23 =>; 0 <=; 0 <~>) % 0.55/0.65 % Maximal formula depth : 9 ( 4 avg) % 0.55/0.65 % Maximal term depth : 3 ( 1 avg) % 0.55/0.65 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.55/0.65 % Number of functors : 7 ( 7 usr; 1 con; 0-2 aty) % 0.55/0.65 % Number of variables : 148 ( 144 !; 4 ?) % 0.55/0.65 % SPC : FOF_THM_RFO_SEQ % 0.55/0.65 % 0.55/0.65 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.55/0.65 % library, www.mizar.org % 0.55/0.65 %------------------------------------------------------------------------------ % 0.55/0.65 fof(antisymmetry_r2_hidden,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( in(A,B) % 0.55/0.65 => ~ in(B,A) ) ). % 0.55/0.65 % 0.55/0.65 fof(antisymmetry_r2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( proper_subset(A,B) % 0.55/0.65 => ~ proper_subset(B,A) ) ). % 0.55/0.65 % 0.55/0.65 fof(commutativity_k2_tarski,axiom, % 0.55/0.65 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.55/0.65 % 0.55/0.65 fof(commutativity_k2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.55/0.65 % 0.55/0.65 fof(commutativity_k3_xboole_0,axiom, % 0.55/0.65 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.55/0.65 % 0.55/0.65 fof(d10_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( A = B % 0.55/0.65 <=> ( subset(A,B) % 0.55/0.65 & subset(B,A) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d1_tarski,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( B = singleton(A) % 0.55/0.65 <=> ! [C] : % 0.55/0.65 ( in(C,B) % 0.55/0.65 <=> C = A ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d1_xboole_0,axiom, % 0.55/0.65 ! [A] : % 0.55/0.65 ( A = empty_set % 0.55/0.65 <=> ! [B] : ~ in(B,A) ) ). % 0.55/0.65 % 0.55/0.65 fof(d1_zfmisc_1,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( B = powerset(A) % 0.55/0.65 <=> ! [C] : % 0.55/0.65 ( in(C,B) % 0.55/0.65 <=> subset(C,A) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d2_tarski,axiom, % 0.55/0.65 ! [A,B,C] : % 0.55/0.65 ( C = unordered_pair(A,B) % 0.55/0.65 <=> ! [D] : % 0.55/0.65 ( in(D,C) % 0.55/0.65 <=> ( D = A % 0.55/0.65 | D = B ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d2_xboole_0,axiom, % 0.55/0.65 ! [A,B,C] : % 0.55/0.65 ( C = set_union2(A,B) % 0.55/0.65 <=> ! [D] : % 0.55/0.65 ( in(D,C) % 0.55/0.65 <=> ( in(D,A) % 0.55/0.65 | in(D,B) ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d3_tarski,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( subset(A,B) % 0.55/0.65 <=> ! [C] : % 0.55/0.65 ( in(C,A) % 0.55/0.65 => in(C,B) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d3_xboole_0,axiom, % 0.55/0.65 ! [A,B,C] : % 0.55/0.65 ( C = set_intersection2(A,B) % 0.55/0.65 <=> ! [D] : % 0.55/0.65 ( in(D,C) % 0.55/0.65 <=> ( in(D,A) % 0.55/0.65 & in(D,B) ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d4_xboole_0,axiom, % 0.55/0.65 ! [A,B,C] : % 0.55/0.65 ( C = set_difference(A,B) % 0.55/0.65 <=> ! [D] : % 0.55/0.65 ( in(D,C) % 0.55/0.65 <=> ( in(D,A) % 0.55/0.65 & ~ in(D,B) ) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(d7_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( disjoint(A,B) % 0.55/0.65 <=> set_intersection2(A,B) = empty_set ) ). % 0.55/0.65 % 0.55/0.65 fof(d8_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( proper_subset(A,B) % 0.55/0.65 <=> ( subset(A,B) % 0.55/0.65 & A != B ) ) ). % 0.55/0.65 % 0.55/0.65 fof(dt_k1_tarski,axiom, % 0.55/0.65 $true ). % 0.55/0.65 % 0.55/0.65 fof(dt_k1_xboole_0,axiom, % 0.55/0.65 $true ). % 0.55/0.65 % 0.55/0.65 fof(dt_k1_zfmisc_1,axiom, % 0.55/0.65 $true ). % 0.55/0.65 % 0.55/0.65 fof(dt_k2_tarski,axiom, % 0.55/0.65 $true ). % 0.55/0.65 % 0.55/0.65 fof(dt_k2_xboole_0,axiom, % 0.55/0.65 $true ). % 0.55/0.65 % 0.55/0.65 fof(dt_k3_xboole_0,axiom, % 0.55/0.65 $true ). % 0.55/0.65 % 0.55/0.65 fof(dt_k4_xboole_0,axiom, % 0.55/0.65 $true ). % 0.55/0.65 % 0.55/0.65 fof(fc1_xboole_0,axiom, % 0.55/0.65 empty(empty_set) ). % 0.55/0.65 % 0.55/0.65 fof(fc2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( ~ empty(A) % 0.55/0.65 => ~ empty(set_union2(A,B)) ) ). % 0.55/0.65 % 0.55/0.65 fof(fc3_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( ~ empty(A) % 0.55/0.65 => ~ empty(set_union2(B,A)) ) ). % 0.55/0.65 % 0.55/0.65 fof(idempotence_k2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : set_union2(A,A) = A ). % 0.55/0.65 % 0.55/0.65 fof(idempotence_k3_xboole_0,axiom, % 0.55/0.65 ! [A,B] : set_intersection2(A,A) = A ). % 0.55/0.65 % 0.55/0.65 fof(irreflexivity_r2_xboole_0,axiom, % 0.55/0.65 ! [A,B] : ~ proper_subset(A,A) ). % 0.55/0.65 % 0.55/0.65 fof(l1_zfmisc_1,lemma, % 0.55/0.65 ! [A] : singleton(A) != empty_set ). % 0.55/0.65 % 0.55/0.65 fof(l23_zfmisc_1,conjecture, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( in(A,B) % 0.55/0.65 => set_union2(singleton(A),B) = B ) ). % 0.55/0.65 % 0.55/0.65 fof(l2_zfmisc_1,lemma, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( subset(singleton(A),B) % 0.55/0.65 <=> in(A,B) ) ). % 0.55/0.65 % 0.55/0.65 fof(l32_xboole_1,lemma, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( set_difference(A,B) = empty_set % 0.55/0.65 <=> subset(A,B) ) ). % 0.55/0.65 % 0.55/0.65 fof(l3_zfmisc_1,lemma, % 0.55/0.65 ! [A,B,C] : % 0.55/0.65 ( subset(A,B) % 0.55/0.65 => ( in(C,A) % 0.55/0.65 | subset(A,set_difference(B,singleton(C))) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(l4_zfmisc_1,lemma, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( subset(A,singleton(B)) % 0.55/0.65 <=> ( A = empty_set % 0.55/0.65 | A = singleton(B) ) ) ). % 0.55/0.65 % 0.55/0.65 fof(rc1_xboole_0,axiom, % 0.55/0.65 ? [A] : empty(A) ). % 0.55/0.65 % 0.55/0.65 fof(rc2_xboole_0,axiom, % 0.55/0.65 ? [A] : ~ empty(A) ). % 0.55/0.65 % 0.55/0.65 fof(reflexivity_r1_tarski,axiom, % 0.55/0.65 ! [A,B] : subset(A,A) ). % 0.55/0.65 % 0.55/0.65 fof(symmetry_r1_xboole_0,axiom, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( disjoint(A,B) % 0.55/0.65 => disjoint(B,A) ) ). % 0.55/0.65 % 0.55/0.65 fof(t10_zfmisc_1,lemma, % 0.55/0.65 ! [A,B,C,D] : % 0.55/0.65 ~ ( unordered_pair(A,B) = unordered_pair(C,D) % 0.55/0.65 & A != C % 0.55/0.65 & A != D ) ). % 0.55/0.65 % 0.55/0.65 fof(t12_xboole_1,lemma, % 0.55/0.65 ! [A,B] : % 0.55/0.65 ( subset(A,B) % 0.55/0.65 => set_union2(A,B) = B ) ). % 0.55/0.65 % 0.55/0.65 fof(t17_xboole_1,lemma, % 0.55/0.65 ! [A,B] : subset(set_intersection2(A,B),A) ). % 0.55/0.65 % 0.55/0.65 fof(t19_xboole_1,lemma, % 0.55/0.65 ! [A,B,C] : % 0.55/0.66 ( ( subset(A,B) % 0.55/0.66 & subset(A,C) ) % 0.55/0.66 => subset(A,set_intersection2(B,C)) ) ). % 0.55/0.66 % 0.55/0.66 fof(t1_boole,axiom, % 0.55/0.66 ! [A] : set_union2(A,empty_set) = A ). % 0.55/0.66 % 0.55/0.66 fof(t1_xboole_1,lemma, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( ( subset(A,B) % 0.55/0.66 & subset(B,C) ) % 0.55/0.66 => subset(A,C) ) ). % 0.55/0.66 % 0.55/0.66 fof(t1_zfmisc_1,lemma, % 0.55/0.66 powerset(empty_set) = singleton(empty_set) ). % 0.55/0.66 % 0.55/0.66 fof(t26_xboole_1,lemma, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( subset(A,B) % 0.55/0.66 => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ). % 0.55/0.66 % 0.55/0.66 fof(t28_xboole_1,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( subset(A,B) % 0.55/0.66 => set_intersection2(A,B) = A ) ). % 0.55/0.66 % 0.55/0.66 fof(t2_boole,axiom, % 0.55/0.66 ! [A] : set_intersection2(A,empty_set) = empty_set ). % 0.55/0.66 % 0.55/0.66 fof(t2_tarski,axiom, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( ! [C] : % 0.55/0.66 ( in(C,A) % 0.55/0.66 <=> in(C,B) ) % 0.55/0.66 => A = B ) ). % 0.55/0.66 % 0.55/0.66 fof(t2_xboole_1,lemma, % 0.55/0.66 ! [A] : subset(empty_set,A) ). % 0.55/0.66 % 0.55/0.66 fof(t33_xboole_1,lemma, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( subset(A,B) % 0.55/0.66 => subset(set_difference(A,C),set_difference(B,C)) ) ). % 0.55/0.66 % 0.55/0.66 fof(t36_xboole_1,lemma, % 0.55/0.66 ! [A,B] : subset(set_difference(A,B),A) ). % 0.55/0.66 % 0.55/0.66 fof(t37_xboole_1,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( set_difference(A,B) = empty_set % 0.55/0.66 <=> subset(A,B) ) ). % 0.55/0.66 % 0.55/0.66 fof(t39_xboole_1,lemma, % 0.55/0.66 ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ). % 0.55/0.66 % 0.55/0.66 fof(t3_boole,axiom, % 0.55/0.66 ! [A] : set_difference(A,empty_set) = A ). % 0.55/0.66 % 0.55/0.66 fof(t3_xboole_0,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( ~ ( ~ disjoint(A,B) % 0.55/0.66 & ! [C] : % 0.55/0.66 ~ ( in(C,A) % 0.55/0.66 & in(C,B) ) ) % 0.55/0.66 & ~ ( ? [C] : % 0.55/0.66 ( in(C,A) % 0.55/0.66 & in(C,B) ) % 0.55/0.66 & disjoint(A,B) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(t3_xboole_1,lemma, % 0.55/0.66 ! [A] : % 0.55/0.66 ( subset(A,empty_set) % 0.55/0.66 => A = empty_set ) ). % 0.55/0.66 % 0.55/0.66 fof(t40_xboole_1,lemma, % 0.55/0.66 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ). % 0.55/0.66 % 0.55/0.66 fof(t45_xboole_1,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( subset(A,B) % 0.55/0.66 => B = set_union2(A,set_difference(B,A)) ) ). % 0.55/0.66 % 0.55/0.66 fof(t48_xboole_1,lemma, % 0.55/0.66 ! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ). % 0.55/0.66 % 0.55/0.66 fof(t4_boole,axiom, % 0.55/0.66 ! [A] : set_difference(empty_set,A) = empty_set ). % 0.55/0.66 % 0.55/0.66 fof(t4_xboole_0,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( ~ ( ~ disjoint(A,B) % 0.55/0.66 & ! [C] : ~ in(C,set_intersection2(A,B)) ) % 0.55/0.66 & ~ ( ? [C] : in(C,set_intersection2(A,B)) % 0.55/0.66 & disjoint(A,B) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(t60_xboole_1,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ~ ( subset(A,B) % 0.55/0.66 & proper_subset(B,A) ) ). % 0.55/0.66 % 0.55/0.66 fof(t63_xboole_1,lemma, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( ( subset(A,B) % 0.55/0.66 & disjoint(B,C) ) % 0.55/0.66 => disjoint(A,C) ) ). % 0.55/0.66 % 0.55/0.66 fof(t69_enumset1,lemma, % 0.55/0.66 ! [A] : unordered_pair(A,A) = singleton(A) ). % 0.55/0.66 % 0.55/0.66 fof(t6_boole,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( empty(A) % 0.55/0.66 => A = empty_set ) ). % 0.55/0.66 % 0.55/0.66 fof(t6_zfmisc_1,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( subset(singleton(A),singleton(B)) % 0.55/0.66 => A = B ) ). % 0.55/0.66 % 0.55/0.66 fof(t7_boole,axiom, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ~ ( in(A,B) % 0.55/0.66 & empty(B) ) ). % 0.55/0.66 % 0.55/0.66 fof(t7_xboole_1,lemma, % 0.55/0.66 ! [A,B] : subset(A,set_union2(A,B)) ). % 0.55/0.66 % 0.55/0.66 fof(t83_xboole_1,lemma, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( disjoint(A,B) % 0.55/0.66 <=> set_difference(A,B) = A ) ). % 0.55/0.66 % 0.55/0.66 fof(t8_boole,axiom, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ~ ( empty(A) % 0.55/0.66 & A != B % 0.55/0.66 & empty(B) ) ). % 0.55/0.66 % 0.55/0.66 fof(t8_xboole_1,lemma, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( ( subset(A,B) % 0.55/0.66 & subset(C,B) ) % 0.55/0.66 => subset(set_union2(A,C),B) ) ). % 0.55/0.66 % 0.55/0.66 fof(t8_zfmisc_1,lemma, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( singleton(A) = unordered_pair(B,C) % 0.55/0.66 => A = B ) ). % 0.55/0.66 % 0.55/0.66 fof(t9_zfmisc_1,lemma, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( singleton(A) = unordered_pair(B,C) % 0.55/0.66 => B = C ) ). % 0.55/0.66 % 0.55/0.66 %------------------------------------------------------------------------------ % 0.55/0.66 %------------------------------------------- % 0.55/0.66 % Proof found % 0.55/0.66 % SZS status Theorem for theBenchmark % 0.55/0.66 % SZS output start Proof % 0.55/0.66 %ClaNum:155(EqnAxiom:44) % 0.55/0.66 %VarNum:607(SingletonVarNum:234) % 0.55/0.66 %MaxLitNum:4 % 0.55/0.66 %MaxfuncDepth:2 % 0.55/0.66 %SharedTerms:15 % 0.55/0.66 %goalClause: 47 68 % 0.55/0.66 %singleGoalClaCount:2 % 0.55/0.66 [45]P1(a1) % 0.55/0.66 [46]P1(a2) % 0.55/0.66 [47]P3(a4,a3) % 0.55/0.66 [65]~P1(a5) % 0.55/0.66 [52]E(f20(a1,a1),f18(a1)) % 0.55/0.66 [68]~E(f19(f20(a4,a4),a3),a3) % 0.55/0.66 [49]P4(a1,x491) % 0.55/0.66 [53]P4(x531,x531) % 0.55/0.66 [67]~P5(x671,x671) % 0.55/0.66 [48]E(f17(a1,x481),a1) % 0.55/0.66 [50]E(f19(x501,a1),x501) % 0.55/0.66 [51]E(f17(x511,a1),x511) % 0.55/0.66 [54]E(f19(x541,x541),x541) % 0.55/0.66 [66]~E(f20(x661,x661),a1) % 0.55/0.66 [57]E(f17(x571,f17(x571,a1)),a1) % 0.55/0.66 [60]E(f17(x601,f17(x601,x601)),x601) % 0.55/0.66 [55]E(f20(x551,x552),f20(x552,x551)) % 0.55/0.66 [56]E(f19(x561,x562),f19(x562,x561)) % 0.55/0.66 [58]P4(x581,f19(x581,x582)) % 0.55/0.66 [59]P4(f17(x591,x592),x591) % 0.55/0.66 [61]E(f19(x611,f17(x612,x611)),f19(x611,x612)) % 0.55/0.66 [62]E(f17(f19(x621,x622),x622),f17(x621,x622)) % 0.55/0.66 [63]E(f17(x631,f17(x631,x632)),f17(x632,f17(x632,x631))) % 0.55/0.66 [69]~P1(x691)+E(x691,a1) % 0.55/0.66 [73]~P4(x731,a1)+E(x731,a1) % 0.55/0.66 [74]P3(f6(x741),x741)+E(x741,a1) % 0.55/0.66 [72]~E(x721,x722)+P4(x721,x722) % 0.55/0.66 [75]~P3(x752,x751)+~E(x751,a1) % 0.55/0.66 [76]~P5(x761,x762)+~E(x761,x762) % 0.55/0.66 [77]~P1(x771)+~P3(x772,x771) % 0.55/0.66 [82]~P5(x821,x822)+P4(x821,x822) % 0.55/0.66 [83]~P2(x832,x831)+P2(x831,x832) % 0.55/0.66 [92]~P3(x922,x921)+~P3(x921,x922) % 0.55/0.66 [93]~P5(x932,x931)+~P5(x931,x932) % 0.55/0.66 [94]~P4(x942,x941)+~P5(x941,x942) % 0.55/0.66 [79]~P4(x791,x792)+E(f17(x791,x792),a1) % 0.55/0.66 [81]P4(x811,x812)+~E(f17(x811,x812),a1) % 0.55/0.66 [84]~P4(x841,x842)+E(f19(x841,x842),x842) % 0.55/0.66 [85]~P2(x851,x852)+E(f17(x851,x852),x851) % 0.55/0.66 [86]P2(x861,x862)+~E(f17(x861,x862),x861) % 0.55/0.66 [91]~E(x911,a1)+P4(x911,f20(x912,x912)) % 0.55/0.66 [103]P1(x1031)+~P1(f19(x1032,x1031)) % 0.55/0.66 [104]P1(x1041)+~P1(f19(x1041,x1042)) % 0.55/0.66 [105]P4(x1051,x1052)+P3(f11(x1051,x1052),x1051) % 0.55/0.66 [106]P2(x1061,x1062)+P3(f7(x1061,x1062),x1062) % 0.55/0.66 [107]P2(x1071,x1072)+P3(f7(x1071,x1072),x1071) % 0.55/0.66 [115]~P3(x1151,x1152)+P4(f20(x1151,x1151),x1152) % 0.55/0.66 [125]P3(x1251,x1252)+~P4(f20(x1251,x1251),x1252) % 0.55/0.66 [126]P4(x1261,x1262)+~P3(f11(x1261,x1262),x1262) % 0.55/0.66 [135]E(x1351,x1352)+~P4(f20(x1351,x1351),f20(x1352,x1352)) % 0.55/0.66 [114]~P2(x1141,x1142)+E(f17(x1141,f17(x1141,x1142)),a1) % 0.55/0.66 [116]~P4(x1161,x1162)+E(f19(x1161,f17(x1162,x1161)),x1162) % 0.55/0.66 [117]~P4(x1171,x1172)+E(f17(x1171,f17(x1171,x1172)),x1171) % 0.55/0.66 [124]P2(x1241,x1242)+~E(f17(x1241,f17(x1241,x1242)),a1) % 0.55/0.66 [140]P2(x1401,x1402)+P3(f10(x1401,x1402),f17(x1401,f17(x1401,x1402))) % 0.55/0.66 [97]E(x971,x972)+~E(f20(x973,x973),f20(x971,x972)) % 0.55/0.66 [98]E(x981,x982)+~E(f20(x981,x981),f20(x982,x983)) % 0.55/0.66 [131]~P4(x1311,x1313)+P4(f17(x1311,x1312),f17(x1313,x1312)) % 0.55/0.66 [142]~P2(x1421,x1422)+~P3(x1423,f17(x1421,f17(x1421,x1422))) % 0.55/0.66 [143]~P4(x1431,x1433)+P4(f17(x1431,f17(x1431,x1432)),f17(x1433,f17(x1433,x1432))) % 0.55/0.66 [70]~P1(x702)+~P1(x701)+E(x701,x702) % 0.55/0.66 [87]P5(x871,x872)+~P4(x871,x872)+E(x871,x872) % 0.55/0.66 [99]~P4(x992,x991)+~P4(x991,x992)+E(x991,x992) % 0.55/0.66 [121]E(f9(x1212,x1211),x1212)+P3(f9(x1212,x1211),x1211)+E(x1211,f20(x1212,x1212)) % 0.55/0.66 [127]E(x1271,f20(x1272,x1272))+~P4(x1271,f20(x1272,x1272))+E(x1271,a1) % 0.55/0.66 [128]E(x1281,x1282)+P3(f8(x1281,x1282),x1282)+P3(f8(x1281,x1282),x1281) % 0.55/0.66 [130]P3(f12(x1302,x1301),x1301)+P4(f12(x1302,x1301),x1302)+E(x1301,f18(x1302)) % 0.55/0.66 [134]~E(f9(x1342,x1341),x1342)+~P3(f9(x1342,x1341),x1341)+E(x1341,f20(x1342,x1342)) % 0.55/0.66 [137]E(x1371,x1372)+~P3(f8(x1371,x1372),x1372)+~P3(f8(x1371,x1372),x1371) % 0.55/0.66 [139]~P3(f12(x1392,x1391),x1391)+~P4(f12(x1392,x1391),x1392)+E(x1391,f18(x1392)) % 0.55/0.66 [108]~P4(x1083,x1082)+P3(x1081,x1082)+~P3(x1081,x1083) % 0.55/0.66 [109]~P4(x1091,x1093)+P4(x1091,x1092)+~P4(x1093,x1092) % 0.55/0.66 [110]~P2(x1103,x1102)+P2(x1101,x1102)+~P4(x1101,x1103) % 0.55/0.66 [119]~P2(x1193,x1192)+~P3(x1191,x1192)+~P3(x1191,x1193) % 0.55/0.66 [95]~P4(x951,x953)+P3(x951,x952)+~E(x952,f18(x953)) % 0.55/0.66 [96]~P3(x961,x963)+P4(x961,x962)+~E(x963,f18(x962)) % 0.55/0.66 [101]~P3(x1011,x1013)+E(x1011,x1012)+~E(x1013,f20(x1012,x1012)) % 0.55/0.66 [129]~P4(x1292,x1293)+~P4(x1291,x1293)+P4(f19(x1291,x1292),x1293) % 0.55/0.66 [145]P3(f15(x1452,x1453,x1451),x1451)+P3(f15(x1452,x1453,x1451),x1452)+E(x1451,f17(x1452,x1453)) % 0.55/0.66 [148]~E(f13(x1482,x1483,x1481),x1483)+~P3(f13(x1482,x1483,x1481),x1481)+E(x1481,f20(x1482,x1483)) % 0.55/0.66 [149]~E(f13(x1492,x1493,x1491),x1492)+~P3(f13(x1492,x1493,x1491),x1491)+E(x1491,f20(x1492,x1493)) % 0.55/0.66 [150]P3(f15(x1502,x1503,x1501),x1501)+~P3(f15(x1502,x1503,x1501),x1503)+E(x1501,f17(x1502,x1503)) % 0.55/0.66 [152]~P3(f14(x1522,x1523,x1521),x1521)+~P3(f14(x1522,x1523,x1521),x1523)+E(x1521,f19(x1522,x1523)) % 0.55/0.66 [153]~P3(f14(x1532,x1533,x1531),x1531)+~P3(f14(x1532,x1533,x1531),x1532)+E(x1531,f19(x1532,x1533)) % 0.55/0.66 [138]~P4(x1382,x1383)+P3(x1381,x1382)+P4(x1382,f17(x1383,f20(x1381,x1381))) % 0.55/0.66 [141]~P4(x1411,x1413)+~P4(x1411,x1412)+P4(x1411,f17(x1412,f17(x1412,x1413))) % 0.55/0.66 [146]P3(f16(x1462,x1463,x1461),x1461)+P3(f16(x1462,x1463,x1461),x1463)+E(x1461,f17(x1462,f17(x1462,x1463))) % 0.55/0.66 [147]P3(f16(x1472,x1473,x1471),x1471)+P3(f16(x1472,x1473,x1471),x1472)+E(x1471,f17(x1472,f17(x1472,x1473))) % 0.55/0.66 [88]P3(x881,x882)+~E(x881,x883)+~E(x882,f20(x884,x883)) % 0.55/0.66 [89]P3(x891,x892)+~E(x891,x893)+~E(x892,f20(x893,x894)) % 0.55/0.66 [100]E(x1001,x1002)+E(x1001,x1003)+~E(f20(x1001,x1004),f20(x1003,x1002)) % 0.55/0.66 [111]~P3(x1111,x1114)+P3(x1111,x1112)+~E(x1112,f19(x1113,x1114)) % 0.55/0.66 [112]~P3(x1121,x1123)+P3(x1121,x1122)+~E(x1122,f19(x1123,x1124)) % 0.55/0.66 [113]~P3(x1131,x1133)+P3(x1131,x1132)+~E(x1133,f17(x1132,x1134)) % 0.55/0.66 [120]~P3(x1204,x1203)+~P3(x1204,x1201)+~E(x1201,f17(x1202,x1203)) % 0.55/0.66 [132]~P3(x1321,x1323)+P3(x1321,x1322)+~E(x1323,f17(x1324,f17(x1324,x1322))) % 0.55/0.66 [144]E(f13(x1442,x1443,x1441),x1443)+E(f13(x1442,x1443,x1441),x1442)+P3(f13(x1442,x1443,x1441),x1441)+E(x1441,f20(x1442,x1443)) % 0.55/0.66 [151]P3(f14(x1512,x1513,x1511),x1511)+P3(f14(x1512,x1513,x1511),x1513)+P3(f14(x1512,x1513,x1511),x1512)+E(x1511,f19(x1512,x1513)) % 0.55/0.66 [154]P3(f15(x1542,x1543,x1541),x1543)+~P3(f15(x1542,x1543,x1541),x1541)+~P3(f15(x1542,x1543,x1541),x1542)+E(x1541,f17(x1542,x1543)) % 0.55/0.66 [155]~P3(f16(x1552,x1553,x1551),x1551)+~P3(f16(x1552,x1553,x1551),x1553)+~P3(f16(x1552,x1553,x1551),x1552)+E(x1551,f17(x1552,f17(x1552,x1553))) % 0.55/0.66 [102]~P3(x1021,x1024)+E(x1021,x1022)+E(x1021,x1023)+~E(x1024,f20(x1023,x1022)) % 0.55/0.66 [122]~P3(x1221,x1224)+P3(x1221,x1222)+P3(x1221,x1223)+~E(x1222,f17(x1224,x1223)) % 0.55/0.66 [123]~P3(x1231,x1234)+P3(x1231,x1232)+P3(x1231,x1233)+~E(x1234,f19(x1233,x1232)) % 0.55/0.66 [136]~P3(x1361,x1364)+~P3(x1361,x1363)+P3(x1361,x1362)+~E(x1362,f17(x1363,f17(x1363,x1364))) % 0.55/0.66 %EqnAxiom % 0.55/0.66 [1]E(x11,x11) % 0.55/0.66 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.66 [4]~E(x41,x42)+E(f17(x41,x43),f17(x42,x43)) % 0.55/0.66 [5]~E(x51,x52)+E(f17(x53,x51),f17(x53,x52)) % 0.55/0.66 [6]~E(x61,x62)+E(f19(x61,x63),f19(x62,x63)) % 0.55/0.66 [7]~E(x71,x72)+E(f19(x73,x71),f19(x73,x72)) % 0.55/0.66 [8]~E(x81,x82)+E(f16(x81,x83,x84),f16(x82,x83,x84)) % 0.55/0.66 [9]~E(x91,x92)+E(f16(x93,x91,x94),f16(x93,x92,x94)) % 0.55/0.66 [10]~E(x101,x102)+E(f16(x103,x104,x101),f16(x103,x104,x102)) % 0.55/0.66 [11]~E(x111,x112)+E(f20(x111,x113),f20(x112,x113)) % 0.55/0.66 [12]~E(x121,x122)+E(f20(x123,x121),f20(x123,x122)) % 0.55/0.66 [13]~E(x131,x132)+E(f18(x131),f18(x132)) % 0.55/0.66 [14]~E(x141,x142)+E(f8(x141,x143),f8(x142,x143)) % 0.55/0.66 [15]~E(x151,x152)+E(f8(x153,x151),f8(x153,x152)) % 0.55/0.66 [16]~E(x161,x162)+E(f13(x161,x163,x164),f13(x162,x163,x164)) % 0.55/0.66 [17]~E(x171,x172)+E(f13(x173,x171,x174),f13(x173,x172,x174)) % 0.55/0.66 [18]~E(x181,x182)+E(f13(x183,x184,x181),f13(x183,x184,x182)) % 0.55/0.66 [19]~E(x191,x192)+E(f15(x191,x193,x194),f15(x192,x193,x194)) % 0.55/0.66 [20]~E(x201,x202)+E(f15(x203,x201,x204),f15(x203,x202,x204)) % 0.55/0.66 [21]~E(x211,x212)+E(f15(x213,x214,x211),f15(x213,x214,x212)) % 0.55/0.66 [22]~E(x221,x222)+E(f7(x221,x223),f7(x222,x223)) % 0.55/0.66 [23]~E(x231,x232)+E(f7(x233,x231),f7(x233,x232)) % 0.55/0.66 [24]~E(x241,x242)+E(f12(x241,x243),f12(x242,x243)) % 0.55/0.66 [25]~E(x251,x252)+E(f12(x253,x251),f12(x253,x252)) % 0.55/0.66 [26]~E(x261,x262)+E(f11(x261,x263),f11(x262,x263)) % 0.55/0.66 [27]~E(x271,x272)+E(f11(x273,x271),f11(x273,x272)) % 0.55/0.66 [28]~E(x281,x282)+E(f10(x281,x283),f10(x282,x283)) % 0.55/0.66 [29]~E(x291,x292)+E(f10(x293,x291),f10(x293,x292)) % 0.55/0.66 [30]~E(x301,x302)+E(f9(x301,x303),f9(x302,x303)) % 0.55/0.66 [31]~E(x311,x312)+E(f9(x313,x311),f9(x313,x312)) % 0.55/0.66 [32]~E(x321,x322)+E(f14(x321,x323,x324),f14(x322,x323,x324)) % 0.55/0.66 [33]~E(x331,x332)+E(f14(x333,x331,x334),f14(x333,x332,x334)) % 0.55/0.66 [34]~E(x341,x342)+E(f14(x343,x344,x341),f14(x343,x344,x342)) % 0.55/0.66 [35]~E(x351,x352)+E(f6(x351),f6(x352)) % 0.55/0.66 [36]~P1(x361)+P1(x362)+~E(x361,x362) % 0.55/0.66 [37]P3(x372,x373)+~E(x371,x372)+~P3(x371,x373) % 0.55/0.66 [38]P3(x383,x382)+~E(x381,x382)+~P3(x383,x381) % 0.55/0.66 [39]P4(x392,x393)+~E(x391,x392)+~P4(x391,x393) % 0.55/0.66 [40]P4(x403,x402)+~E(x401,x402)+~P4(x403,x401) % 0.55/0.66 [41]P2(x412,x413)+~E(x411,x412)+~P2(x411,x413) % 0.55/0.66 [42]P2(x423,x422)+~E(x421,x422)+~P2(x423,x421) % 0.55/0.66 [43]P5(x432,x433)+~E(x431,x432)+~P5(x431,x433) % 0.55/0.66 [44]P5(x443,x442)+~E(x441,x442)+~P5(x443,x441) % 0.55/0.66 % 0.55/0.66 %------------------------------------------- % 0.55/0.67 cnf(186,plain, % 0.55/0.67 ($false), % 0.55/0.67 inference(scs_inference,[],[47,68,54,46,66,75,74,77,84,92,115]), % 0.55/0.67 ['proof']). % 0.55/0.67 % SZS output end Proof % 0.55/0.67 % Total time :0.000000s %------------------------------------------------------------------------------