%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:03 AM UTC 2026 % Result : Theorem 2.77s 3.10s % Output : Proof 2.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.34 % Computer : n016.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Sat Sep 5 05:45:29 UTC 2026 % 0.07/0.35 % CPUTime : % 0.12/0.43 %----Proving TF0_NAR, FOF, or CNF % 2.77/3.10 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.77/3.10 % SZS status Theorem % 2.77/3.10 % SZS output start Proof % 2.77/3.10 ( % 2.77/3.10 (declare-sort $$unsorted 0) % 2.77/3.10 (declare-const tptp.op_strict_implies Bool) % 2.77/3.10 (declare-const tptp.op_possibly Bool) % 2.77/3.10 (declare-const tptp.axiom_m10 Bool) % 2.77/3.10 (declare-const tptp.axiom_m9 Bool) % 2.77/3.10 (declare-const tptp.axiom_m7 Bool) % 2.77/3.10 (declare-const tptp.axiom_m6 Bool) % 2.77/3.10 (declare-const tptp.r2 Bool) % 2.77/3.10 (declare-const tptp.r1 Bool) % 2.77/3.10 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 2.77/3.10 (declare-const tptp.op_necessarily Bool) % 2.77/3.10 (declare-const tptp.kn3 Bool) % 2.77/3.10 (declare-const tptp.strict_equiv (-> $$unsorted $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.cn2 Bool) % 2.77/3.10 (declare-const tptp.axiom_m3 Bool) % 2.77/3.10 (declare-const tptp.kn2 Bool) % 2.77/3.10 (declare-const tptp.cn1 Bool) % 2.77/3.10 (declare-const tptp.or_2 Bool) % 2.77/3.10 (declare-const tptp.and_3 Bool) % 2.77/3.10 (declare-const tptp.r5 Bool) % 2.77/3.10 (declare-const tptp.necessitation Bool) % 2.77/3.10 (declare-const tptp.equivalence_1 Bool) % 2.77/3.10 (declare-const tptp.implies_1 Bool) % 2.77/3.10 (declare-const tptp.equivalence_2 Bool) % 2.77/3.10 (declare-const tptp.or_3 Bool) % 2.77/3.10 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.substitution_of_equivalents Bool) % 2.77/3.10 (declare-const tptp.implies_3 Bool) % 2.77/3.10 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.axiom_m1 Bool) % 2.77/3.10 (declare-const tptp.and_1 Bool) % 2.77/3.10 (declare-const tptp.equivalence_3 Bool) % 2.77/3.10 (declare-const tptp.necessarily (-> $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.or_1 Bool) % 2.77/3.10 (declare-const tptp.op_or Bool) % 2.77/3.10 (declare-const tptp.cn3 Bool) % 2.77/3.10 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.op_strict_equiv Bool) % 2.77/3.10 (declare-const tptp.axiom_4 Bool) % 2.77/3.10 (declare-const tptp.modus_tollens Bool) % 2.77/3.10 (declare-const tptp.and_2 Bool) % 2.77/3.10 (declare-const tptp.implies_2 Bool) % 2.77/3.10 (declare-const tptp.axiom_5 Bool) % 2.77/3.10 (declare-const tptp.axiom_s2 Bool) % 2.77/3.10 (declare-const tptp.r4 Bool) % 2.77/3.10 (declare-const tptp.kn1 Bool) % 2.77/3.10 (declare-const tptp.adjunction Bool) % 2.77/3.10 (declare-const tptp.modus_ponens Bool) % 2.77/3.10 (declare-const tptp.op_and Bool) % 2.77/3.10 (declare-const tptp.axiom_M Bool) % 2.77/3.10 (declare-const tptp.possibly (-> $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.op_equiv Bool) % 2.77/3.10 (declare-const tptp.strict_implies (-> $$unsorted $$unsorted $$unsorted)) % 2.77/3.10 (declare-const tptp.axiom_m8 Bool) % 2.77/3.10 (declare-const tptp.modus_ponens_strict_implies Bool) % 2.77/3.10 (declare-const tptp.substitution_strict_equiv Bool) % 2.77/3.10 (declare-const tptp.axiom_K Bool) % 2.77/3.10 (declare-const tptp.op_implies Bool) % 2.77/3.10 (declare-const tptp.axiom_B Bool) % 2.77/3.10 (declare-const tptp.axiom_s1 Bool) % 2.77/3.10 (declare-const tptp.r3 Bool) % 2.77/3.10 (declare-const tptp.axiom_s3 Bool) % 2.77/3.10 (declare-const tptp.axiom_s4 Bool) % 2.77/3.10 (declare-const tptp.axiom_m2 Bool) % 2.77/3.10 (declare-const tptp.op_implies_and Bool) % 2.77/3.10 (declare-const tptp.axiom_m4 Bool) % 2.77/3.10 (declare-const tptp.op_implies_or Bool) % 2.77/3.10 (declare-const tptp.axiom_m5 Bool) % 2.77/3.10 (define @t1 () (@var "Y" $$unsorted)) % 2.77/3.10 (define @t2 () (tptp.is_a_theorem @t1)) % 2.77/3.10 (define @t3 () (@var "X" $$unsorted)) % 2.77/3.10 (define @t4 () (tptp.implies @t3 @t1)) % 2.77/3.10 (define @t5 () (tptp.is_a_theorem @t4)) % 2.77/3.10 (define @t6 () (tptp.is_a_theorem @t3)) % 2.77/3.10 (define @t7 () (and @t6 @t5)) % 2.77/3.10 (define @t8 () (@list @t3 @t1)) % 2.77/3.10 (define @t9 () (forall @t8 (=> @t7 @t2))) % 2.77/3.10 (define @t10 () (= tptp.modus_ponens @t9)) % 2.77/3.10 (define @t11 () (= @t3 @t1)) % 2.77/3.10 (define @t12 () (tptp.equiv @t3 @t1)) % 2.77/3.10 (define @t13 () (tptp.not @t3)) % 2.77/3.10 (define @t14 () (tptp.not @t1)) % 2.77/3.10 (define @t15 () (tptp.implies @t1 @t3)) % 2.77/3.10 (define @t16 () (@var "Z" $$unsorted)) % 2.77/3.10 (define @t17 () (tptp.implies @t3 @t16)) % 2.77/3.10 (define @t18 () (tptp.implies @t1 @t16)) % 2.77/3.10 (define @t19 () (@list @t3 @t1 @t16)) % 2.77/3.10 (define @t20 () (tptp.and @t3 @t1)) % 2.77/3.10 (define @t21 () (tptp.or @t3 @t1)) % 2.77/3.10 (define @t22 () (@var "P" $$unsorted)) % 2.77/3.10 (define @t23 () (@list @t22)) % 2.77/3.10 (define @t24 () (@var "Q" $$unsorted)) % 2.77/3.10 (define @t25 () (tptp.and @t22 @t24)) % 2.77/3.10 (define @t26 () (@list @t22 @t24)) % 2.77/3.10 (define @t27 () (@var "R" $$unsorted)) % 2.77/3.10 (define @t28 () (tptp.implies @t22 @t24)) % 2.77/3.10 (define @t29 () (@list @t22 @t24 @t27)) % 2.77/3.10 (define @t30 () (tptp.implies @t24 @t27)) % 2.77/3.10 (define @t31 () (tptp.not @t22)) % 2.77/3.10 (define @t32 () (tptp.or @t22 @t24)) % 2.77/3.10 (define @t33 () (tptp.or @t22 @t27)) % 2.77/3.10 (define @t34 () (tptp.necessarily @t3)) % 2.77/3.10 (define @t35 () (@list @t3)) % 2.77/3.10 (define @t36 () (tptp.strict_implies @t3 @t1)) % 2.77/3.10 (define @t37 () (tptp.is_a_theorem @t36)) % 2.77/3.10 (define @t38 () (and @t6 @t37)) % 2.77/3.10 (define @t39 () (forall @t8 (=> @t38 @t2))) % 2.77/3.10 (define @t40 () (= tptp.modus_ponens_strict_implies @t39)) % 2.77/3.10 (define @t41 () (tptp.strict_equiv @t3 @t1)) % 2.77/3.10 (define @t42 () (tptp.necessarily @t4)) % 2.77/3.10 (define @t43 () (forall @t35 (tptp.is_a_theorem (tptp.implies @t34 @t3)))) % 2.77/3.10 (define @t44 () (tptp.necessarily @t34)) % 2.77/3.10 (define @t45 () (tptp.possibly @t3)) % 2.77/3.10 (define @t46 () (tptp.necessarily @t45)) % 2.77/3.10 (define @t47 () (tptp.possibly @t24)) % 2.77/3.10 (define @t48 () (tptp.possibly @t22)) % 2.77/3.10 (define @t49 () (tptp.possibly @t25)) % 2.77/3.10 (define @t50 () (forall @t8 (= @t36 @t42))) % 2.77/3.10 (define @t51 () (not @t5)) % 2.77/3.10 (define @t52 () (not @t6)) % 2.77/3.10 (define @t53 () (or @t52 @t51 @t2)) % 2.77/3.10 (define @t54 () (forall @t8 @t53)) % 2.77/3.10 (define @t55 () (@list false)) % 2.77/3.10 (define @t56 () (not @t37)) % 2.77/3.10 (define @t57 () (or @t52 @t56 @t2)) % 2.77/3.10 (define @t58 () (forall @t8 @t57)) % 2.77/3.10 (define @t59 () (@quantifiers_skolemize @t58 1)) % 2.77/3.10 (define @t60 () (@quantifiers_skolemize @t58 0)) % 2.77/3.10 (define @t61 () (tptp.implies @t60 @t59)) % 2.77/3.10 (define @t62 () (tptp.necessarily @t61)) % 2.77/3.10 (define @t63 () (@list @t60 @t59)) % 2.77/3.10 (define @t64 () (@list true)) % 2.77/3.10 (define @t65 () (tptp.is_a_theorem @t59)) % 2.77/3.10 (define @t66 () (tptp.is_a_theorem (tptp.strict_implies @t60 @t59))) % 2.77/3.10 (define @t67 () (not @t66)) % 2.77/3.10 (define @t68 () (tptp.is_a_theorem @t60)) % 2.77/3.10 (define @t69 () (not @t68)) % 2.77/3.10 (define @t70 () (or @t69 @t67 @t65)) % 2.77/3.10 (define @t71 () (@list @t70)) % 2.77/3.10 (define @t72 () (tptp.is_a_theorem @t61)) % 2.77/3.10 (define @t73 () (not @t72)) % 2.77/3.10 (define @t74 () (or @t69 @t73 @t65)) % 2.77/3.10 (define @t75 () (tptp.is_a_theorem (tptp.implies @t62 @t61))) % 2.77/3.10 (define @t76 () (not @t75)) % 2.77/3.10 (define @t77 () (not (tptp.is_a_theorem @t62))) % 2.77/3.10 (define @t78 () (or @t77 @t76 @t72)) % 2.77/3.10 (assume @p1 @t10) % 2.77/3.10 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t12) @t11)))) % 2.77/3.10 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t14 @t13) @t4))))) % 2.77/3.10 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t15))))) % 2.77/3.10 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 2.77/3.10 (assume @p6 (= tptp.implies_3 (forall @t19 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t18 @t17)))))) % 2.77/3.10 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t3))))) % 2.77/3.10 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t1))))) % 2.77/3.10 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t20)))))) % 2.77/3.10 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t21))))) % 2.77/3.10 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t21))))) % 2.77/3.10 (assume @p12 (= tptp.or_3 (forall @t19 (tptp.is_a_theorem (tptp.implies @t17 (tptp.implies @t18 (tptp.implies @t21 @t16))))))) % 2.77/3.10 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t4))))) % 2.77/3.10 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t15))))) % 2.77/3.10 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t15 @t12)))))) % 2.77/3.10 (assume @p16 (= tptp.kn1 (forall @t23 (tptp.is_a_theorem (tptp.implies @t22 (tptp.and @t22 @t22)))))) % 2.77/3.10 (assume @p17 (= tptp.kn2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t25 @t22))))) % 2.77/3.10 (assume @p18 (= tptp.kn3 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies (tptp.not (tptp.and @t24 @t27)) (tptp.not (tptp.and @t27 @t22)))))))) % 2.77/3.10 (assume @p19 (= tptp.cn1 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies @t30 (tptp.implies @t22 @t27))))))) % 2.77/3.10 (assume @p20 (= tptp.cn2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t22 (tptp.implies @t31 @t24)))))) % 2.77/3.10 (assume @p21 (= tptp.cn3 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.implies @t31 @t22) @t22))))) % 2.77/3.10 (assume @p22 (= tptp.r1 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 @t22) @t22))))) % 2.77/3.10 (assume @p23 (= tptp.r2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t24 @t32))))) % 2.77/3.10 (assume @p24 (= tptp.r3 (forall @t26 (tptp.is_a_theorem (tptp.implies @t32 (tptp.or @t24 @t22)))))) % 2.77/3.10 (assume @p25 (= tptp.r4 (forall @t29 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 (tptp.or @t24 @t27)) (tptp.or @t24 @t33)))))) % 2.77/3.10 (assume @p26 (= tptp.r5 (forall @t29 (tptp.is_a_theorem (tptp.implies @t30 (tptp.implies @t32 @t33)))))) % 2.77/3.10 (assume @p27 (=> tptp.op_or (forall @t8 (= @t21 (tptp.not (tptp.and @t13 @t14)))))) % 2.77/3.10 (assume @p28 (=> tptp.op_and (forall @t8 (= @t20 (tptp.not (tptp.or @t13 @t14)))))) % 2.77/3.10 (assume @p29 (=> tptp.op_implies_and (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t14)))))) % 2.77/3.10 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t13 @t1))))) % 2.77/3.10 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t12 (tptp.and @t4 @t15))))) % 2.77/3.10 (assume @p32 tptp.op_or) % 2.77/3.10 (assume @p33 tptp.op_implies_and) % 2.77/3.10 (assume @p34 tptp.op_equiv) % 2.77/3.10 (assume @p35 tptp.modus_ponens) % 2.77/3.10 (assume @p36 tptp.modus_tollens) % 2.77/3.10 (assume @p37 tptp.implies_1) % 2.77/3.10 (assume @p38 tptp.implies_2) % 2.77/3.10 (assume @p39 tptp.implies_3) % 2.77/3.10 (assume @p40 tptp.and_1) % 2.77/3.10 (assume @p41 tptp.and_2) % 2.77/3.10 (assume @p42 tptp.and_3) % 2.77/3.10 (assume @p43 tptp.or_1) % 2.77/3.10 (assume @p44 tptp.or_2) % 2.77/3.10 (assume @p45 tptp.or_3) % 2.77/3.10 (assume @p46 tptp.equivalence_1) % 2.77/3.10 (assume @p47 tptp.equivalence_2) % 2.77/3.10 (assume @p48 tptp.equivalence_3) % 2.77/3.10 (assume @p49 tptp.substitution_of_equivalents) % 2.77/3.10 (assume @p50 (= tptp.necessitation (forall @t35 (=> @t6 (tptp.is_a_theorem @t34))))) % 2.77/3.10 (assume @p51 @t40) % 2.77/3.10 (assume @p52 (= tptp.adjunction (forall @t8 (=> (and @t6 @t2) (tptp.is_a_theorem @t20))))) % 2.77/3.10 (assume @p53 (= tptp.substitution_strict_equiv (forall @t8 (=> (tptp.is_a_theorem @t41) @t11)))) % 2.77/3.10 (assume @p54 (= tptp.axiom_K (forall @t8 (tptp.is_a_theorem (tptp.implies @t42 (tptp.implies @t34 (tptp.necessarily @t1))))))) % 2.77/3.10 (assume @p55 (= tptp.axiom_M @t43)) % 2.77/3.10 (assume @p56 (= tptp.axiom_4 (forall @t35 (tptp.is_a_theorem (tptp.implies @t34 @t44))))) % 2.77/3.10 (assume @p57 (= tptp.axiom_B (forall @t35 (tptp.is_a_theorem (tptp.implies @t3 @t46))))) % 2.77/3.10 (assume @p58 (= tptp.axiom_5 (forall @t35 (tptp.is_a_theorem (tptp.implies @t45 @t46))))) % 2.77/3.10 (assume @p59 (= tptp.axiom_s1 (forall @t19 (tptp.is_a_theorem (tptp.implies (tptp.and @t42 (tptp.necessarily @t18)) (tptp.necessarily @t17)))))) % 2.77/3.10 (assume @p60 (= tptp.axiom_s2 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies @t49 (tptp.and @t48 @t47)))))) % 2.77/3.10 (assume @p61 (= tptp.axiom_s3 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t36 (tptp.strict_implies (tptp.not (tptp.possibly @t1)) (tptp.not @t45))))))) % 2.77/3.10 (assume @p62 (= tptp.axiom_s4 (forall @t35 (tptp.is_a_theorem (tptp.strict_implies @t34 @t44))))) % 2.77/3.10 (assume @p63 (= tptp.axiom_m1 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t20 (tptp.and @t1 @t3)))))) % 2.77/3.10 (assume @p64 (= tptp.axiom_m2 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t20 @t3))))) % 2.77/3.10 (assume @p65 (= tptp.axiom_m3 (forall @t19 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t20 @t16) (tptp.and @t3 (tptp.and @t1 @t16))))))) % 2.77/3.10 (assume @p66 (= tptp.axiom_m4 (forall @t35 (tptp.is_a_theorem (tptp.strict_implies @t3 (tptp.and @t3 @t3)))))) % 2.77/3.10 (assume @p67 (= tptp.axiom_m5 (forall @t19 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t36 (tptp.strict_implies @t1 @t16)) (tptp.strict_implies @t3 @t16)))))) % 2.77/3.10 (assume @p68 (= tptp.axiom_m6 (forall @t35 (tptp.is_a_theorem (tptp.strict_implies @t3 @t45))))) % 2.77/3.10 (assume @p69 (= tptp.axiom_m7 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies @t49 @t22))))) % 2.77/3.10 (assume @p70 (= tptp.axiom_m8 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies (tptp.strict_implies @t22 @t24) (tptp.strict_implies @t48 @t47)))))) % 2.77/3.10 (assume @p71 (= tptp.axiom_m9 (forall @t35 (tptp.is_a_theorem (tptp.strict_implies (tptp.possibly @t45) @t45))))) % 2.77/3.10 (assume @p72 (= tptp.axiom_m10 (forall @t35 (tptp.is_a_theorem (tptp.strict_implies @t45 @t46))))) % 2.77/3.10 (assume @p73 (=> tptp.op_possibly (forall @t35 (= @t45 (tptp.not (tptp.necessarily @t13)))))) % 2.77/3.10 (assume @p74 (=> tptp.op_necessarily (forall @t35 (= @t34 (tptp.not (tptp.possibly @t13)))))) % 2.77/3.10 (assume @p75 (=> tptp.op_strict_implies @t50)) % 2.77/3.10 (assume @p76 (=> tptp.op_strict_equiv (forall @t8 (= @t41 (tptp.and @t36 (tptp.strict_implies @t1 @t3)))))) % 2.77/3.10 (assume @p77 tptp.op_possibly) % 2.77/3.10 (assume @p78 tptp.necessitation) % 2.77/3.10 (assume @p79 tptp.axiom_K) % 2.77/3.10 (assume @p80 tptp.axiom_M) % 2.77/3.10 (assume @p81 tptp.axiom_4) % 2.77/3.10 (assume @p82 tptp.axiom_B) % 2.77/3.10 (assume @p83 tptp.op_implies) % 2.77/3.10 (assume @p84 tptp.op_strict_implies) % 2.77/3.10 (assume @p85 tptp.op_strict_equiv) % 2.77/3.10 (assume @p86 (not tptp.modus_ponens_strict_implies)) % 2.77/3.10 (assume @p87 true) % 2.77/3.10 (step @p88 :rule evaluate :args ((= true false))) % 2.77/3.10 (step @p89 :rule aci_norm :args ((= (or (or @t52 @t51) @t2) @t53))) % 2.77/3.10 (step @p90 :rule refl :args (@t2)) % 2.77/3.10 (step @p91 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 2.77/3.10 (step @p92 :rule nary_cong :premises (@p91 @p90) :args ((or (not @t7) @t2))) % 2.77/3.10 (step @p93 :rule trans :premises (@p92 @p89)) % 2.77/3.10 (step @p94 :rule bool-impl-elim :args (@t7 @t2)) % 2.77/3.10 (step @p95 :rule trans :premises (@p94 @p93)) % 2.77/3.10 (step @p96 :rule cong :premises (@p95) :args (@t9)) % 2.77/3.10 (step @p97 :rule refl :args (tptp.modus_ponens)) % 2.77/3.10 (step @p98 :rule cong :premises (@p97 @p96) :args (@t10)) % 2.77/3.10 (step @p99 :rule eq_resolve :premises (@p1 @p98)) % 2.77/3.10 (step @p100 :rule equiv_elim1 :premises (@p99)) % 2.77/3.10 (step @p101 :rule reordering :premises (@p100) :args ((or @t54 (not tptp.modus_ponens)))) % 2.77/3.10 (step @p102 :rule chain_m_resolution :premises (@p101 @p35) :args (@t54 @t55 (@list tptp.modus_ponens))) % 2.77/3.10 (step @p103 :rule instantiate :premises (@p102) :args ((@list @t62 @t61))) % 2.77/3.10 (step @p104 :rule equiv_elim1 :premises (@p55)) % 2.77/3.10 (step @p105 :rule reordering :premises (@p104) :args ((or @t43 (not tptp.axiom_M)))) % 2.77/3.10 (step @p106 :rule chain_m_resolution :premises (@p105 @p80) :args (@t43 @t55 (@list tptp.axiom_M))) % 2.77/3.10 (step @p107 :rule instantiate :premises (@p106) :args ((@list @t61))) % 2.77/3.10 (step @p108 :rule instantiate :premises (@p102) :args (@t63)) % 2.77/3.10 (step @p109 :rule aci_norm :args ((= (or (or @t52 @t56) @t2) @t57))) % 2.77/3.10 (step @p110 :rule bool-and-de-morgan :args (@t6 @t37 true)) % 2.77/3.10 (step @p111 :rule nary_cong :premises (@p110 @p90) :args ((or (not @t38) @t2))) % 2.77/3.10 (step @p112 :rule trans :premises (@p111 @p109)) % 2.77/3.10 (step @p113 :rule bool-impl-elim :args (@t38 @t2)) % 2.77/3.10 (step @p114 :rule trans :premises (@p113 @p112)) % 2.77/3.10 (step @p115 :rule cong :premises (@p114) :args (@t39)) % 2.77/3.10 (step @p116 :rule refl :args (tptp.modus_ponens_strict_implies)) % 2.77/3.10 (step @p117 :rule cong :premises (@p116 @p115) :args (@t40)) % 2.77/3.10 (step @p118 :rule eq_resolve :premises (@p51 @p117)) % 2.77/3.10 (step @p119 :rule equiv_elim2 :premises (@p118)) % 2.77/3.10 (step @p120 :rule chain_m_resolution :premises (@p119 @p86) :args ((not @t58) @t64 (@list tptp.modus_ponens_strict_implies))) % 2.77/3.10 (step @p121 :rule skolemize :premises (@p120)) % 2.77/3.10 (step @p122 :rule cnf_or_neg :args (@t70 2)) % 2.77/3.10 (step @p123 :rule chain_m_resolution :premises (@p122 @p121) :args ((not @t65) @t64 @t71)) % 2.77/3.10 (step @p124 :rule bool-double-not-elim :args (@t68)) % 2.77/3.10 (step @p125 :rule refl :args (@t70)) % 2.77/3.10 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or @t70 (not @t69)))) % 2.77/3.10 (step @p127 :rule cnf_or_neg :args (@t70 0)) % 2.77/3.10 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 2.77/3.10 (step @p129 :rule reordering :premises (@p128) :args ((or @t68 @t70))) % 2.77/3.10 (step @p130 :rule chain_m_resolution :premises (@p129 @p121) :args (@t68 @t64 @t71)) % 2.77/3.10 (step @p131 :rule cnf_or_pos :args (@t74)) % 2.77/3.10 (step @p132 :rule reordering :premises (@p131) :args ((or @t69 @t65 @t73 (not @t74)))) % 2.77/3.10 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p123 @p108) :args (@t73 (@list false true false) (@list @t68 @t65 @t74))) % 2.77/3.10 (step @p134 :rule cnf_or_pos :args (@t78)) % 2.77/3.10 (step @p135 :rule reordering :premises (@p134) :args ((or @t72 @t76 @t77 (not @t78)))) % 2.77/3.10 (step @p136 :rule chain_m_resolution :premises (@p135 @p133 @p107 @p103) :args (@t77 (@list true false false) (@list @t72 @t75 @t78))) % 2.77/3.10 (step @p137 :rule false_intro :premises (@p136)) % 2.77/3.10 (step @p138 :rule implies_elim :premises (@p75)) % 2.77/3.10 (step @p139 :rule reordering :premises (@p138) :args ((or @t50 (not tptp.op_strict_implies)))) % 2.77/3.10 (step @p140 :rule chain_m_resolution :premises (@p139 @p84) :args (@t50 @t55 (@list tptp.op_strict_implies))) % 2.77/3.10 (step @p141 :rule instantiate :premises (@p140) :args (@t63)) % 2.77/3.10 (step @p142 :rule cong :premises (@p141) :args (@t66)) % 2.77/3.10 (step @p143 :rule bool-double-not-elim :args (@t66)) % 2.77/3.10 (step @p144 :rule nary_cong :premises (@p125 @p143) :args ((or @t70 (not @t67)))) % 2.77/3.12 (step @p145 :rule cnf_or_neg :args (@t70 1)) % 2.77/3.12 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 2.77/3.12 (step @p147 :rule reordering :premises (@p146) :args ((or @t66 @t70))) % 2.77/3.12 (step @p148 :rule chain_m_resolution :premises (@p147 @p121) :args (@t66 @t64 @t71)) % 2.77/3.12 (step @p149 :rule true_intro :premises (@p148)) % 2.77/3.12 (step @p150 :rule symm :premises (@p149)) % 2.77/3.12 (step @p151 :rule trans :premises (@p150 @p142 @p137)) % 2.77/3.12 (step @p152 false :rule eq_resolve :premises (@p151 @p88)) % 2.77/3.12 ) % 2.77/3.12 % SZS output end Proof % 2.77/3.12 % cvc5 exiting %------------------------------------------------------------------------------