%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU143+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 : n029.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 15:01:17 EDT 2024 % Result : Theorem 0.52s 0.67s % Output : CNFRefutation 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU143+2 : TPTP v8.2.0. Released v3.3.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Jun 21 18:09:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.52/0.65 %------------------------------------------- % 0.52/0.65 % File :CSE---1.7 % 0.52/0.65 % Problem :theBenchmark % 0.52/0.65 % Transform :cnf % 0.52/0.65 % Format :tptp:raw % 0.52/0.65 % Command :java -jar mcs_scs.jar %d %s % 0.52/0.65 % 0.52/0.65 % Result :Theorem 0.040000s % 0.52/0.65 % Output :CNFRefutation 0.040000s % 0.52/0.65 %------------------------------------------- % 0.52/0.65 %------------------------------------------------------------------------------ % 0.52/0.65 % File : SEU143+2 : TPTP v8.2.0. Released v3.3.0. % 0.52/0.65 % Domain : Set theory % 0.52/0.65 % Problem : MPTP chainy problem l1_zfmisc_1 % 0.52/0.65 % Version : [Urb07] axioms : Especial. % 0.52/0.65 % English : % 0.52/0.65 % 0.52/0.65 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 0.52/0.65 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 0.52/0.65 % Source : [Urb07] % 0.52/0.65 % Names : chainy-l1_zfmisc_1 [Urb07] % 0.52/0.65 % 0.52/0.65 % Status : Theorem % 0.52/0.65 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.30 v5.5.0, 0.26 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.17 v3.7.0, 0.15 v3.5.0, 0.16 v3.3.0 % 0.52/0.65 % Syntax : Number of formulae : 64 ( 29 unt; 0 def) % 0.52/0.66 % Number of atoms : 123 ( 36 equ) % 0.52/0.66 % Maximal formula atoms : 6 ( 1 avg) % 0.52/0.66 % Number of connectives : 83 ( 24 ~; 2 |; 20 &) % 0.52/0.66 % ( 19 <=>; 18 =>; 0 <=; 0 <~>) % 0.52/0.66 % Maximal formula depth : 9 ( 4 avg) % 0.52/0.66 % Maximal term depth : 3 ( 1 avg) % 0.52/0.66 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.52/0.66 % Number of functors : 6 ( 6 usr; 1 con; 0-2 aty) % 0.52/0.66 % Number of variables : 124 ( 120 !; 4 ?) % 0.52/0.66 % SPC : FOF_THM_RFO_SEQ % 0.52/0.66 % 0.52/0.66 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.52/0.66 % library, www.mizar.org % 0.52/0.66 %------------------------------------------------------------------------------ % 0.52/0.66 fof(antisymmetry_r2_hidden,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( in(A,B) % 0.52/0.66 => ~ in(B,A) ) ). % 0.52/0.66 % 0.52/0.66 fof(antisymmetry_r2_xboole_0,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( proper_subset(A,B) % 0.52/0.66 => ~ proper_subset(B,A) ) ). % 0.52/0.66 % 0.52/0.66 fof(commutativity_k2_tarski,axiom, % 0.52/0.66 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.52/0.66 % 0.52/0.66 fof(commutativity_k2_xboole_0,axiom, % 0.52/0.66 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.52/0.66 % 0.52/0.66 fof(commutativity_k3_xboole_0,axiom, % 0.52/0.66 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.52/0.66 % 0.52/0.66 fof(d10_xboole_0,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( A = B % 0.52/0.66 <=> ( subset(A,B) % 0.52/0.66 & subset(B,A) ) ) ). % 0.52/0.66 % 0.52/0.66 fof(d1_tarski,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( B = singleton(A) % 0.52/0.66 <=> ! [C] : % 0.52/0.66 ( in(C,B) % 0.52/0.66 <=> C = A ) ) ). % 0.52/0.66 % 0.52/0.66 fof(d1_xboole_0,axiom, % 0.52/0.66 ! [A] : % 0.52/0.66 ( A = empty_set % 0.52/0.66 <=> ! [B] : ~ in(B,A) ) ). % 0.52/0.66 % 0.52/0.66 fof(d2_tarski,axiom, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( C = unordered_pair(A,B) % 0.52/0.66 <=> ! [D] : % 0.52/0.66 ( in(D,C) % 0.52/0.66 <=> ( D = A % 0.52/0.66 | D = B ) ) ) ). % 0.52/0.66 % 0.52/0.66 fof(d2_xboole_0,axiom, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( C = set_union2(A,B) % 0.52/0.66 <=> ! [D] : % 0.52/0.66 ( in(D,C) % 0.52/0.66 <=> ( in(D,A) % 0.52/0.66 | in(D,B) ) ) ) ). % 0.52/0.66 % 0.52/0.66 fof(d3_tarski,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( subset(A,B) % 0.52/0.66 <=> ! [C] : % 0.52/0.66 ( in(C,A) % 0.52/0.66 => in(C,B) ) ) ). % 0.52/0.66 % 0.52/0.66 fof(d3_xboole_0,axiom, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( C = set_intersection2(A,B) % 0.52/0.66 <=> ! [D] : % 0.52/0.66 ( in(D,C) % 0.52/0.66 <=> ( in(D,A) % 0.52/0.66 & in(D,B) ) ) ) ). % 0.52/0.66 % 0.52/0.66 fof(d4_xboole_0,axiom, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( C = set_difference(A,B) % 0.52/0.66 <=> ! [D] : % 0.52/0.66 ( in(D,C) % 0.52/0.66 <=> ( in(D,A) % 0.52/0.66 & ~ in(D,B) ) ) ) ). % 0.52/0.66 % 0.52/0.66 fof(d7_xboole_0,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( disjoint(A,B) % 0.52/0.66 <=> set_intersection2(A,B) = empty_set ) ). % 0.52/0.66 % 0.52/0.66 fof(d8_xboole_0,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( proper_subset(A,B) % 0.52/0.66 <=> ( subset(A,B) % 0.52/0.66 & A != B ) ) ). % 0.52/0.66 % 0.52/0.66 fof(dt_k1_tarski,axiom, % 0.52/0.66 $true ). % 0.52/0.66 % 0.52/0.66 fof(dt_k1_xboole_0,axiom, % 0.52/0.66 $true ). % 0.52/0.66 % 0.52/0.66 fof(dt_k2_tarski,axiom, % 0.52/0.66 $true ). % 0.52/0.66 % 0.52/0.66 fof(dt_k2_xboole_0,axiom, % 0.52/0.66 $true ). % 0.52/0.66 % 0.52/0.66 fof(dt_k3_xboole_0,axiom, % 0.52/0.66 $true ). % 0.52/0.66 % 0.52/0.66 fof(dt_k4_xboole_0,axiom, % 0.52/0.66 $true ). % 0.52/0.66 % 0.52/0.66 fof(fc1_xboole_0,axiom, % 0.52/0.66 empty(empty_set) ). % 0.52/0.66 % 0.52/0.66 fof(fc2_xboole_0,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( ~ empty(A) % 0.52/0.66 => ~ empty(set_union2(A,B)) ) ). % 0.52/0.66 % 0.52/0.66 fof(fc3_xboole_0,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( ~ empty(A) % 0.52/0.66 => ~ empty(set_union2(B,A)) ) ). % 0.52/0.66 % 0.52/0.66 fof(idempotence_k2_xboole_0,axiom, % 0.52/0.66 ! [A,B] : set_union2(A,A) = A ). % 0.52/0.66 % 0.52/0.66 fof(idempotence_k3_xboole_0,axiom, % 0.52/0.66 ! [A,B] : set_intersection2(A,A) = A ). % 0.52/0.66 % 0.52/0.66 fof(irreflexivity_r2_xboole_0,axiom, % 0.52/0.66 ! [A,B] : ~ proper_subset(A,A) ). % 0.52/0.66 % 0.52/0.66 fof(l1_zfmisc_1,conjecture, % 0.52/0.66 ! [A] : singleton(A) != empty_set ). % 0.52/0.66 % 0.52/0.66 fof(l32_xboole_1,lemma, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( set_difference(A,B) = empty_set % 0.52/0.66 <=> subset(A,B) ) ). % 0.52/0.66 % 0.52/0.66 fof(rc1_xboole_0,axiom, % 0.52/0.66 ? [A] : empty(A) ). % 0.52/0.66 % 0.52/0.66 fof(rc2_xboole_0,axiom, % 0.52/0.66 ? [A] : ~ empty(A) ). % 0.52/0.66 % 0.52/0.66 fof(reflexivity_r1_tarski,axiom, % 0.52/0.66 ! [A,B] : subset(A,A) ). % 0.52/0.66 % 0.52/0.66 fof(symmetry_r1_xboole_0,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( disjoint(A,B) % 0.52/0.66 => disjoint(B,A) ) ). % 0.52/0.66 % 0.52/0.66 fof(t12_xboole_1,lemma, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( subset(A,B) % 0.52/0.66 => set_union2(A,B) = B ) ). % 0.52/0.66 % 0.52/0.66 fof(t17_xboole_1,lemma, % 0.52/0.66 ! [A,B] : subset(set_intersection2(A,B),A) ). % 0.52/0.66 % 0.52/0.66 fof(t19_xboole_1,lemma, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( ( subset(A,B) % 0.52/0.66 & subset(A,C) ) % 0.52/0.66 => subset(A,set_intersection2(B,C)) ) ). % 0.52/0.66 % 0.52/0.66 fof(t1_boole,axiom, % 0.52/0.66 ! [A] : set_union2(A,empty_set) = A ). % 0.52/0.66 % 0.52/0.66 fof(t1_xboole_1,lemma, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( ( subset(A,B) % 0.52/0.66 & subset(B,C) ) % 0.52/0.66 => subset(A,C) ) ). % 0.52/0.66 % 0.52/0.66 fof(t26_xboole_1,lemma, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( subset(A,B) % 0.52/0.66 => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ). % 0.52/0.66 % 0.52/0.66 fof(t28_xboole_1,lemma, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( subset(A,B) % 0.52/0.66 => set_intersection2(A,B) = A ) ). % 0.52/0.66 % 0.52/0.66 fof(t2_boole,axiom, % 0.52/0.66 ! [A] : set_intersection2(A,empty_set) = empty_set ). % 0.52/0.66 % 0.52/0.66 fof(t2_tarski,axiom, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( ! [C] : % 0.52/0.66 ( in(C,A) % 0.52/0.66 <=> in(C,B) ) % 0.52/0.66 => A = B ) ). % 0.52/0.66 % 0.52/0.66 fof(t2_xboole_1,lemma, % 0.52/0.66 ! [A] : subset(empty_set,A) ). % 0.52/0.66 % 0.52/0.66 fof(t33_xboole_1,lemma, % 0.52/0.66 ! [A,B,C] : % 0.52/0.66 ( subset(A,B) % 0.52/0.66 => subset(set_difference(A,C),set_difference(B,C)) ) ). % 0.52/0.66 % 0.52/0.66 fof(t36_xboole_1,lemma, % 0.52/0.66 ! [A,B] : subset(set_difference(A,B),A) ). % 0.52/0.66 % 0.52/0.66 fof(t37_xboole_1,lemma, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( set_difference(A,B) = empty_set % 0.52/0.66 <=> subset(A,B) ) ). % 0.52/0.66 % 0.52/0.66 fof(t39_xboole_1,lemma, % 0.52/0.66 ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ). % 0.52/0.66 % 0.52/0.66 fof(t3_boole,axiom, % 0.52/0.66 ! [A] : set_difference(A,empty_set) = A ). % 0.52/0.66 % 0.52/0.66 fof(t3_xboole_0,lemma, % 0.52/0.66 ! [A,B] : % 0.52/0.66 ( ~ ( ~ disjoint(A,B) % 0.52/0.66 & ! [C] : % 0.52/0.66 ~ ( in(C,A) % 0.52/0.66 & in(C,B) ) ) % 0.52/0.66 & ~ ( ? [C] : % 0.52/0.66 ( in(C,A) % 0.52/0.66 & in(C,B) ) % 0.52/0.66 & disjoint(A,B) ) ) ). % 0.52/0.66 % 0.52/0.66 fof(t3_xboole_1,lemma, % 0.52/0.66 ! [A] : % 0.52/0.66 ( subset(A,empty_set) % 0.52/0.66 => A = empty_set ) ). % 0.52/0.67 % 0.52/0.67 fof(t40_xboole_1,lemma, % 0.52/0.67 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ). % 0.52/0.67 % 0.52/0.67 fof(t45_xboole_1,lemma, % 0.52/0.67 ! [A,B] : % 0.52/0.67 ( subset(A,B) % 0.52/0.67 => B = set_union2(A,set_difference(B,A)) ) ). % 0.52/0.67 % 0.52/0.67 fof(t48_xboole_1,lemma, % 0.52/0.67 ! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ). % 0.52/0.67 % 0.52/0.67 fof(t4_boole,axiom, % 0.52/0.67 ! [A] : set_difference(empty_set,A) = empty_set ). % 0.52/0.67 % 0.52/0.67 fof(t4_xboole_0,lemma, % 0.52/0.67 ! [A,B] : % 0.52/0.67 ( ~ ( ~ disjoint(A,B) % 0.52/0.67 & ! [C] : ~ in(C,set_intersection2(A,B)) ) % 0.52/0.67 & ~ ( ? [C] : in(C,set_intersection2(A,B)) % 0.52/0.67 & disjoint(A,B) ) ) ). % 0.52/0.67 % 0.52/0.67 fof(t60_xboole_1,lemma, % 0.52/0.67 ! [A,B] : % 0.52/0.67 ~ ( subset(A,B) % 0.52/0.67 & proper_subset(B,A) ) ). % 0.52/0.67 % 0.52/0.67 fof(t63_xboole_1,lemma, % 0.52/0.67 ! [A,B,C] : % 0.52/0.67 ( ( subset(A,B) % 0.52/0.67 & disjoint(B,C) ) % 0.52/0.67 => disjoint(A,C) ) ). % 0.52/0.67 % 0.52/0.67 fof(t69_enumset1,lemma, % 0.52/0.67 ! [A] : unordered_pair(A,A) = singleton(A) ). % 0.52/0.67 % 0.52/0.67 fof(t6_boole,axiom, % 0.52/0.67 ! [A] : % 0.52/0.67 ( empty(A) % 0.52/0.67 => A = empty_set ) ). % 0.52/0.67 % 0.52/0.67 fof(t7_boole,axiom, % 0.52/0.67 ! [A,B] : % 0.52/0.67 ~ ( in(A,B) % 0.52/0.67 & empty(B) ) ). % 0.52/0.67 % 0.52/0.67 fof(t7_xboole_1,lemma, % 0.52/0.67 ! [A,B] : subset(A,set_union2(A,B)) ). % 0.52/0.67 % 0.52/0.67 fof(t83_xboole_1,lemma, % 0.52/0.67 ! [A,B] : % 0.52/0.67 ( disjoint(A,B) % 0.52/0.67 <=> set_difference(A,B) = A ) ). % 0.52/0.67 % 0.52/0.67 fof(t8_boole,axiom, % 0.52/0.67 ! [A,B] : % 0.52/0.67 ~ ( empty(A) % 0.52/0.67 & A != B % 0.52/0.67 & empty(B) ) ). % 0.52/0.67 % 0.52/0.67 fof(t8_xboole_1,lemma, % 0.52/0.67 ! [A,B,C] : % 0.52/0.67 ( ( subset(A,B) % 0.52/0.67 & subset(C,B) ) % 0.52/0.67 => subset(set_union2(A,C),B) ) ). % 0.52/0.67 % 0.52/0.67 %------------------------------------------------------------------------------ % 0.52/0.67 %------------------------------------------- % 0.52/0.67 % Proof found % 0.52/0.67 % SZS status Theorem for theBenchmark % 0.52/0.67 % SZS output start Proof % 0.52/0.67 %ClaNum:135(EqnAxiom:41) % 0.52/0.67 %VarNum:522(SingletonVarNum:200) % 0.52/0.67 %MaxLitNum:4 % 0.52/0.67 %MaxfuncDepth:2 % 0.52/0.67 %SharedTerms:9 % 0.52/0.67 %goalClause: 44 % 0.52/0.67 %singleGoalClaCount:1 % 0.52/0.67 [42]P1(a1) % 0.52/0.67 [43]P1(a2) % 0.52/0.67 [61]~P1(a4) % 0.52/0.67 [44]E(f15(a3,a3),a1) % 0.52/0.67 [46]P3(a1,x461) % 0.52/0.67 [49]P3(x491,x491) % 0.52/0.67 [62]~P4(x621,x621) % 0.52/0.67 [45]E(f16(a1,x451),a1) % 0.52/0.67 [47]E(f17(x471,a1),x471) % 0.52/0.67 [48]E(f16(x481,a1),x481) % 0.52/0.67 [50]E(f17(x501,x501),x501) % 0.52/0.67 [53]E(f16(x531,f16(x531,a1)),a1) % 0.52/0.67 [56]E(f16(x561,f16(x561,x561)),x561) % 0.52/0.67 [51]E(f15(x511,x512),f15(x512,x511)) % 0.52/0.67 [52]E(f17(x521,x522),f17(x522,x521)) % 0.52/0.67 [54]P3(x541,f17(x541,x542)) % 0.52/0.67 [55]P3(f16(x551,x552),x551) % 0.52/0.67 [57]E(f17(x571,f16(x572,x571)),f17(x571,x572)) % 0.52/0.67 [58]E(f16(f17(x581,x582),x582),f16(x581,x582)) % 0.52/0.67 [59]E(f16(x591,f16(x591,x592)),f16(x592,f16(x592,x591))) % 0.52/0.67 [63]~P1(x631)+E(x631,a1) % 0.52/0.67 [67]~P3(x671,a1)+E(x671,a1) % 0.52/0.67 [68]P5(f5(x681),x681)+E(x681,a1) % 0.52/0.67 [66]~E(x661,x662)+P3(x661,x662) % 0.52/0.67 [69]~P5(x692,x691)+~E(x691,a1) % 0.52/0.67 [70]~P4(x701,x702)+~E(x701,x702) % 0.52/0.67 [71]~P1(x711)+~P5(x712,x711) % 0.52/0.67 [76]~P4(x761,x762)+P3(x761,x762) % 0.52/0.67 [77]~P2(x772,x771)+P2(x771,x772) % 0.52/0.67 [85]~P5(x852,x851)+~P5(x851,x852) % 0.52/0.67 [86]~P4(x862,x861)+~P4(x861,x862) % 0.52/0.67 [87]~P3(x872,x871)+~P4(x871,x872) % 0.52/0.67 [73]~P3(x731,x732)+E(f16(x731,x732),a1) % 0.52/0.67 [75]P3(x751,x752)+~E(f16(x751,x752),a1) % 0.52/0.67 [78]~P3(x781,x782)+E(f17(x781,x782),x782) % 0.52/0.67 [79]~P2(x791,x792)+E(f16(x791,x792),x791) % 0.52/0.67 [80]P2(x801,x802)+~E(f16(x801,x802),x801) % 0.52/0.67 [91]P1(x911)+~P1(f17(x912,x911)) % 0.52/0.67 [92]P1(x921)+~P1(f17(x921,x922)) % 0.52/0.67 [93]P3(x931,x932)+P5(f10(x931,x932),x931) % 0.52/0.67 [94]P2(x941,x942)+P5(f6(x941,x942),x942) % 0.52/0.67 [95]P2(x951,x952)+P5(f6(x951,x952),x951) % 0.52/0.67 [111]P3(x1111,x1112)+~P5(f10(x1111,x1112),x1112) % 0.52/0.67 [102]~P2(x1021,x1022)+E(f16(x1021,f16(x1021,x1022)),a1) % 0.52/0.67 [103]~P3(x1031,x1032)+E(f17(x1031,f16(x1032,x1031)),x1032) % 0.52/0.67 [104]~P3(x1041,x1042)+E(f16(x1041,f16(x1041,x1042)),x1041) % 0.52/0.67 [110]P2(x1101,x1102)+~E(f16(x1101,f16(x1101,x1102)),a1) % 0.52/0.67 [120]P2(x1201,x1202)+P5(f9(x1201,x1202),f16(x1201,f16(x1201,x1202))) % 0.52/0.67 [114]~P3(x1141,x1143)+P3(f16(x1141,x1142),f16(x1143,x1142)) % 0.52/0.67 [122]~P2(x1221,x1222)+~P5(x1223,f16(x1221,f16(x1221,x1222))) % 0.52/0.67 [123]~P3(x1231,x1233)+P3(f16(x1231,f16(x1231,x1232)),f16(x1233,f16(x1233,x1232))) % 0.52/0.67 [64]~P1(x642)+~P1(x641)+E(x641,x642) % 0.52/0.67 [81]P4(x811,x812)+~P3(x811,x812)+E(x811,x812) % 0.52/0.67 [88]~P3(x882,x881)+~P3(x881,x882)+E(x881,x882) % 0.52/0.67 [107]E(f8(x1072,x1071),x1072)+P5(f8(x1072,x1071),x1071)+E(x1071,f15(x1072,x1072)) % 0.52/0.67 [112]E(x1121,x1122)+P5(f7(x1121,x1122),x1122)+P5(f7(x1121,x1122),x1121) % 0.52/0.67 [117]~E(f8(x1172,x1171),x1172)+~P5(f8(x1172,x1171),x1171)+E(x1171,f15(x1172,x1172)) % 0.52/0.67 [119]E(x1191,x1192)+~P5(f7(x1191,x1192),x1192)+~P5(f7(x1191,x1192),x1191) % 0.52/0.67 [96]~P3(x963,x962)+P5(x961,x962)+~P5(x961,x963) % 0.52/0.67 [97]~P3(x971,x973)+P3(x971,x972)+~P3(x973,x972) % 0.52/0.67 [98]~P2(x983,x982)+P2(x981,x982)+~P3(x981,x983) % 0.52/0.67 [105]~P2(x1053,x1052)+~P5(x1051,x1052)+~P5(x1051,x1053) % 0.52/0.67 [89]~P5(x891,x893)+E(x891,x892)+~E(x893,f15(x892,x892)) % 0.52/0.67 [113]~P3(x1132,x1133)+~P3(x1131,x1133)+P3(f17(x1131,x1132),x1133) % 0.52/0.67 [125]P5(f13(x1252,x1253,x1251),x1251)+P5(f13(x1252,x1253,x1251),x1252)+E(x1251,f16(x1252,x1253)) % 0.52/0.67 [128]~E(f11(x1282,x1283,x1281),x1283)+~P5(f11(x1282,x1283,x1281),x1281)+E(x1281,f15(x1282,x1283)) % 0.52/0.67 [129]~E(f11(x1292,x1293,x1291),x1292)+~P5(f11(x1292,x1293,x1291),x1291)+E(x1291,f15(x1292,x1293)) % 0.52/0.67 [130]P5(f13(x1302,x1303,x1301),x1301)+~P5(f13(x1302,x1303,x1301),x1303)+E(x1301,f16(x1302,x1303)) % 0.52/0.67 [132]~P5(f12(x1322,x1323,x1321),x1321)+~P5(f12(x1322,x1323,x1321),x1323)+E(x1321,f17(x1322,x1323)) % 0.52/0.67 [133]~P5(f12(x1332,x1333,x1331),x1331)+~P5(f12(x1332,x1333,x1331),x1332)+E(x1331,f17(x1332,x1333)) % 0.52/0.67 [121]~P3(x1211,x1213)+~P3(x1211,x1212)+P3(x1211,f16(x1212,f16(x1212,x1213))) % 0.52/0.67 [126]P5(f14(x1262,x1263,x1261),x1261)+P5(f14(x1262,x1263,x1261),x1263)+E(x1261,f16(x1262,f16(x1262,x1263))) % 0.52/0.67 [127]P5(f14(x1272,x1273,x1271),x1271)+P5(f14(x1272,x1273,x1271),x1272)+E(x1271,f16(x1272,f16(x1272,x1273))) % 0.52/0.67 [82]P5(x821,x822)+~E(x821,x823)+~E(x822,f15(x824,x823)) % 0.52/0.67 [83]P5(x831,x832)+~E(x831,x833)+~E(x832,f15(x833,x834)) % 0.52/0.67 [99]~P5(x991,x994)+P5(x991,x992)+~E(x992,f17(x993,x994)) % 0.52/0.67 [100]~P5(x1001,x1003)+P5(x1001,x1002)+~E(x1002,f17(x1003,x1004)) % 0.52/0.67 [101]~P5(x1011,x1013)+P5(x1011,x1012)+~E(x1013,f16(x1012,x1014)) % 0.52/0.67 [106]~P5(x1064,x1063)+~P5(x1064,x1061)+~E(x1061,f16(x1062,x1063)) % 0.52/0.67 [115]~P5(x1151,x1153)+P5(x1151,x1152)+~E(x1153,f16(x1154,f16(x1154,x1152))) % 0.52/0.67 [124]E(f11(x1242,x1243,x1241),x1243)+E(f11(x1242,x1243,x1241),x1242)+P5(f11(x1242,x1243,x1241),x1241)+E(x1241,f15(x1242,x1243)) % 0.52/0.67 [131]P5(f12(x1312,x1313,x1311),x1311)+P5(f12(x1312,x1313,x1311),x1313)+P5(f12(x1312,x1313,x1311),x1312)+E(x1311,f17(x1312,x1313)) % 0.52/0.67 [134]P5(f13(x1342,x1343,x1341),x1343)+~P5(f13(x1342,x1343,x1341),x1341)+~P5(f13(x1342,x1343,x1341),x1342)+E(x1341,f16(x1342,x1343)) % 0.52/0.67 [135]~P5(f14(x1352,x1353,x1351),x1351)+~P5(f14(x1352,x1353,x1351),x1353)+~P5(f14(x1352,x1353,x1351),x1352)+E(x1351,f16(x1352,f16(x1352,x1353))) % 0.52/0.67 [90]~P5(x901,x904)+E(x901,x902)+E(x901,x903)+~E(x904,f15(x903,x902)) % 0.52/0.67 [108]~P5(x1081,x1084)+P5(x1081,x1082)+P5(x1081,x1083)+~E(x1082,f16(x1084,x1083)) % 0.52/0.67 [109]~P5(x1091,x1094)+P5(x1091,x1092)+P5(x1091,x1093)+~E(x1094,f17(x1093,x1092)) % 0.52/0.67 [118]~P5(x1181,x1184)+~P5(x1181,x1183)+P5(x1181,x1182)+~E(x1182,f16(x1183,f16(x1183,x1184))) % 0.52/0.67 %EqnAxiom % 0.52/0.67 [1]E(x11,x11) % 0.52/0.67 [2]E(x22,x21)+~E(x21,x22) % 0.52/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.52/0.67 [4]~E(x41,x42)+E(f15(x41,x43),f15(x42,x43)) % 0.52/0.67 [5]~E(x51,x52)+E(f15(x53,x51),f15(x53,x52)) % 0.52/0.67 [6]~E(x61,x62)+E(f16(x61,x63),f16(x62,x63)) % 0.52/0.67 [7]~E(x71,x72)+E(f16(x73,x71),f16(x73,x72)) % 0.52/0.67 [8]~E(x81,x82)+E(f17(x81,x83),f17(x82,x83)) % 0.52/0.67 [9]~E(x91,x92)+E(f17(x93,x91),f17(x93,x92)) % 0.52/0.67 [10]~E(x101,x102)+E(f12(x101,x103,x104),f12(x102,x103,x104)) % 0.52/0.67 [11]~E(x111,x112)+E(f12(x113,x111,x114),f12(x113,x112,x114)) % 0.52/0.67 [12]~E(x121,x122)+E(f12(x123,x124,x121),f12(x123,x124,x122)) % 0.52/0.67 [13]~E(x131,x132)+E(f10(x131,x133),f10(x132,x133)) % 0.52/0.67 [14]~E(x141,x142)+E(f10(x143,x141),f10(x143,x142)) % 0.52/0.67 [15]~E(x151,x152)+E(f14(x151,x153,x154),f14(x152,x153,x154)) % 0.52/0.67 [16]~E(x161,x162)+E(f14(x163,x161,x164),f14(x163,x162,x164)) % 0.52/0.67 [17]~E(x171,x172)+E(f14(x173,x174,x171),f14(x173,x174,x172)) % 0.52/0.67 [18]~E(x181,x182)+E(f11(x181,x183,x184),f11(x182,x183,x184)) % 0.52/0.67 [19]~E(x191,x192)+E(f11(x193,x191,x194),f11(x193,x192,x194)) % 0.52/0.67 [20]~E(x201,x202)+E(f11(x203,x204,x201),f11(x203,x204,x202)) % 0.52/0.67 [21]~E(x211,x212)+E(f7(x211,x213),f7(x212,x213)) % 0.52/0.67 [22]~E(x221,x222)+E(f7(x223,x221),f7(x223,x222)) % 0.52/0.67 [23]~E(x231,x232)+E(f13(x231,x233,x234),f13(x232,x233,x234)) % 0.52/0.67 [24]~E(x241,x242)+E(f13(x243,x241,x244),f13(x243,x242,x244)) % 0.52/0.67 [25]~E(x251,x252)+E(f13(x253,x254,x251),f13(x253,x254,x252)) % 0.52/0.67 [26]~E(x261,x262)+E(f6(x261,x263),f6(x262,x263)) % 0.52/0.67 [27]~E(x271,x272)+E(f6(x273,x271),f6(x273,x272)) % 0.52/0.67 [28]~E(x281,x282)+E(f8(x281,x283),f8(x282,x283)) % 0.52/0.67 [29]~E(x291,x292)+E(f8(x293,x291),f8(x293,x292)) % 0.52/0.67 [30]~E(x301,x302)+E(f9(x301,x303),f9(x302,x303)) % 0.52/0.67 [31]~E(x311,x312)+E(f9(x313,x311),f9(x313,x312)) % 0.52/0.67 [32]~E(x321,x322)+E(f5(x321),f5(x322)) % 0.52/0.67 [33]~P1(x331)+P1(x332)+~E(x331,x332) % 0.52/0.67 [34]P5(x342,x343)+~E(x341,x342)+~P5(x341,x343) % 0.52/0.67 [35]P5(x353,x352)+~E(x351,x352)+~P5(x353,x351) % 0.52/0.67 [36]P3(x362,x363)+~E(x361,x362)+~P3(x361,x363) % 0.52/0.67 [37]P3(x373,x372)+~E(x371,x372)+~P3(x373,x371) % 0.52/0.67 [38]P2(x382,x383)+~E(x381,x382)+~P2(x381,x383) % 0.52/0.67 [39]P2(x393,x392)+~E(x391,x392)+~P2(x393,x391) % 0.52/0.67 [40]P4(x402,x403)+~E(x401,x402)+~P4(x401,x403) % 0.52/0.67 [41]P4(x413,x412)+~E(x411,x412)+~P4(x413,x411) % 0.52/0.67 % 0.52/0.67 %------------------------------------------- % 0.52/0.67 cnf(137,plain, % 0.52/0.67 (~P5(x1371,a1)), % 0.52/0.67 inference(equality_inference,[],[69])). % 0.52/0.67 cnf(141,plain, % 0.52/0.67 (~P5(x1411,x1412)+P5(x1411,f17(x1413,x1412))), % 0.52/0.67 inference(equality_inference,[],[99])). % 0.52/0.67 cnf(142,plain, % 0.52/0.67 (~P5(x1421,x1422)+P5(x1421,f17(x1422,x1423))), % 0.52/0.67 inference(equality_inference,[],[100])). % 0.52/0.67 cnf(143,plain, % 0.52/0.67 (~P5(x1431,f16(x1432,x1433))+P5(x1431,x1432)), % 0.52/0.67 inference(equality_inference,[],[101])). % 0.52/0.67 cnf(144,plain, % 0.52/0.67 (~P5(x1441,x1442)+~P5(x1441,f16(x1443,x1442))), % 0.52/0.67 inference(equality_inference,[],[106])). % 0.52/0.67 cnf(145,plain, % 0.52/0.67 (~P5(x1451,x1452)+P5(x1451,f16(x1452,x1453))+P5(x1451,x1453)), % 0.52/0.67 inference(equality_inference,[],[108])). % 0.52/0.67 cnf(146,plain, % 0.52/0.67 (~P5(x1461,f17(x1462,x1463))+P5(x1461,x1463)+P5(x1461,x1462)), % 0.52/0.67 inference(equality_inference,[],[109])). % 0.52/0.67 cnf(147,plain, % 0.52/0.67 (~P5(x1471,f16(x1472,f16(x1472,x1473)))+P5(x1471,x1473)), % 0.52/0.67 inference(equality_inference,[],[115])). % 0.52/0.67 cnf(149,plain, % 0.52/0.67 (~P5(x1491,f15(a3,a3))), % 0.52/0.67 inference(scs_inference,[],[44,69])). % 0.52/0.67 cnf(153,plain, % 0.52/0.67 (E(a1,f15(a3,a3))), % 0.52/0.67 inference(scs_inference,[],[44,69,70,2])). % 0.52/0.67 cnf(156,plain, % 0.52/0.67 (P3(x1561,f16(x1561,a1))), % 0.52/0.67 inference(scs_inference,[],[44,43,53,69,70,2,71,75])). % 0.52/0.67 cnf(165,plain, % 0.52/0.67 (~P5(x1651,a1)), % 0.52/0.67 inference(rename_variables,[],[137])). % 0.52/0.67 cnf(169,plain, % 0.52/0.67 (~P5(x1691,f16(x1692,f16(x1692,a1)))), % 0.52/0.67 inference(scs_inference,[],[44,137,165,48,43,53,69,70,2,71,75,80,93,94,95,143,147])). % 0.52/0.67 cnf(172,plain, % 0.52/0.67 (E(f17(x1721,x1721),x1721)), % 0.52/0.67 inference(rename_variables,[],[50])). % 0.52/0.67 cnf(174,plain, % 0.52/0.67 (P5(f15(a3,a3),f17(f15(a1,x1741),f15(a1,x1741)))), % 0.52/0.67 inference(scs_inference,[],[44,137,165,50,172,48,43,53,69,70,2,71,75,80,93,94,95,143,147,82,83])). % 0.52/0.67 cnf(175,plain, % 0.52/0.67 (E(f17(x1751,x1751),x1751)), % 0.52/0.67 inference(rename_variables,[],[50])). % 0.52/0.67 cnf(177,plain, % 0.52/0.67 (E(f17(f15(a3,a3),f15(a3,a3)),a1)), % 0.52/0.67 inference(scs_inference,[],[44,137,165,50,172,175,48,43,53,69,70,2,71,75,80,93,94,95,143,147,82,83,3])). % 0.52/0.67 cnf(178,plain, % 0.52/0.67 (E(f17(x1781,x1781),x1781)), % 0.52/0.67 inference(rename_variables,[],[50])). % 0.52/0.67 cnf(180,plain, % 0.52/0.67 (E(f17(x1801,x1801),x1801)), % 0.52/0.67 inference(rename_variables,[],[50])). % 0.52/0.67 cnf(181,plain, % 0.52/0.67 (P5(a1,f17(f15(x1811,a1),f15(x1811,a1)))), % 0.52/0.67 inference(scs_inference,[],[44,137,165,50,172,175,178,48,43,61,53,69,70,2,71,75,80,93,94,95,143,147,82,83,3,33,34])). % 0.52/0.67 cnf(183,plain, % 0.52/0.67 (~P5(x1831,a1)), % 0.52/0.67 inference(rename_variables,[],[137])). % 0.52/0.67 cnf(184,plain, % 0.52/0.67 (P3(f16(f15(a3,a3),x1841),a1)), % 0.52/0.67 inference(scs_inference,[],[44,137,165,50,172,175,178,55,48,43,61,53,69,70,2,71,75,80,93,94,95,143,147,82,83,3,33,34,35,37])). % 0.52/0.67 cnf(185,plain, % 0.52/0.67 (P3(f16(x1851,x1852),x1851)), % 0.52/0.67 inference(rename_variables,[],[55])). % 0.52/0.67 cnf(186,plain, % 0.52/0.67 (P2(f15(a3,a3),x1861)), % 0.52/0.67 inference(scs_inference,[],[44,137,165,50,172,175,178,55,48,43,61,53,69,70,2,71,75,80,93,94,95,143,147,82,83,3,33,34,35,37,38])). % 0.52/0.67 cnf(197,plain, % 0.52/0.67 (E(f17(x1971,x1972),f17(x1972,x1971))), % 0.52/0.67 inference(rename_variables,[],[52])). % 0.52/0.67 cnf(203,plain, % 0.52/0.67 (E(f17(x2031,x2031),x2031)), % 0.52/0.67 inference(rename_variables,[],[50])). % 0.52/0.67 cnf(206,plain, % 0.52/0.67 (~P5(x2061,a1)), % 0.52/0.67 inference(rename_variables,[],[137])). % 0.52/0.67 cnf(209,plain, % 0.52/0.67 (E(f17(x2091,a1),x2091)), % 0.52/0.67 inference(rename_variables,[],[47])). % 0.52/0.67 cnf(212,plain, % 0.52/0.67 (~P5(x2121,a1)), % 0.52/0.67 inference(rename_variables,[],[137])). % 0.52/0.67 cnf(237,plain, % 0.52/0.67 (~P3(f15(x2371,a1),a1)), % 0.52/0.67 inference(scs_inference,[],[44,137,165,183,206,212,49,46,50,172,175,178,180,203,51,52,197,55,185,47,209,48,42,43,61,53,69,70,2,71,75,80,93,94,95,143,147,82,83,3,33,34,35,37,38,39,64,88,89,99,100,101,112,115,145,146,90,109,67,76,141,142,144,36,81,113])). % 0.52/0.67 cnf(246,plain, % 0.52/0.67 (P5(f5(f15(x2461,a1)),f15(x2461,a1))), % 0.52/0.67 inference(scs_inference,[],[44,137,165,183,206,212,49,46,50,172,175,178,180,203,51,52,197,55,185,47,209,48,42,43,61,53,69,70,2,71,75,80,93,94,95,143,147,82,83,3,33,34,35,37,38,39,64,88,89,99,100,101,112,115,145,146,90,109,67,76,141,142,144,36,81,113,131,66,63,68])). % 0.52/0.67 cnf(253,plain, % 0.52/0.67 (~P5(x2531,f16(x2532,f16(x2532,a1)))), % 0.52/0.67 inference(rename_variables,[],[169])). % 0.52/0.67 cnf(256,plain, % 0.52/0.67 (~P5(x2561,f16(x2562,f16(x2562,a1)))), % 0.52/0.67 inference(rename_variables,[],[169])). % 0.52/0.67 cnf(283,plain, % 0.52/0.67 (P3(x2831,f16(x2831,a1))), % 0.52/0.67 inference(rename_variables,[],[156])). % 0.52/0.67 cnf(291,plain, % 0.52/0.67 ($false), % 0.52/0.67 inference(scs_inference,[],[149,186,174,181,184,177,153,137,169,253,256,156,283,246,237,56,55,95,94,142,69,85,143,141,144,70,147,76,93,80,2,96,97,98,83]), % 0.52/0.67 ['proof']). % 0.52/0.67 % SZS output end Proof % 0.52/0.67 % Total time :0.040000s %------------------------------------------------------------------------------