%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG257^1 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.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 : Wed Jun 3 08:05:40 AM UTC 2026 % Result : Theorem 0.41s 0.80s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG257^1 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n001.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 01:55:50 EDT 2026 % 0.17/0.34 % CPUTime : % 0.38/0.57 %----Proving TH0 % 0.41/0.80 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.80 % SZS status Theorem % 0.41/0.80 % SZS output start Proof % 0.41/0.80 ( % 0.41/0.80 (declare-sort tptp.term 0) % 0.41/0.80 (declare-sort tptp.subst 0) % 0.41/0.80 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 0.41/0.80 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 0.41/0.80 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 0.41/0.80 (declare-const tptp.one tptp.term) % 0.41/0.80 (declare-const tptp.sh tptp.subst) % 0.41/0.80 (declare-const tptp.lam (-> tptp.term tptp.term)) % 0.41/0.80 (declare-const tptp.var (-> tptp.term Bool)) % 0.41/0.80 (declare-const tptp.id tptp.subst) % 0.41/0.80 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lthm_3 Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3b Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3a Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3 Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3aaa Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3aa Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem2 Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem1 Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3v2a Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3v2 Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem2v2 Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem1v2 Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasinduction_lem0 Bool) % 0.41/0.80 (declare-const tptp.hoasapnotvar_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasapnotvar_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasapnotvar Bool) % 0.41/0.80 (declare-const tptp.hoaslamnotvar_lthm Bool) % 0.41/0.80 (declare-const tptp.hoaslamnotvar_gthm Bool) % 0.41/0.80 (declare-const tptp.hoaslamnotvar Bool) % 0.41/0.80 (declare-const tptp.hoaslamnotap_lthm Bool) % 0.41/0.80 (declare-const tptp.hoaslamnotap_gthm Bool) % 0.41/0.80 (declare-const tptp.hoaslamnotap Bool) % 0.41/0.80 (declare-const tptp.hoaslaminj_lthm Bool) % 0.41/0.80 (declare-const tptp.hoaslaminj_gthm Bool) % 0.41/0.80 (declare-const tptp.hoaslaminj Bool) % 0.41/0.80 (declare-const tptp.hoasapinj2_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasapinj2_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasapinj2 Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem0_lthm Bool) % 0.41/0.80 (declare-const tptp.axassoc Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem0_gthm Bool) % 0.41/0.80 (declare-const tptp.axvarcons Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem0 Bool) % 0.41/0.80 (declare-const tptp.apinj1 Bool) % 0.41/0.80 (declare-const tptp.induction Bool) % 0.41/0.80 (declare-const tptp.apnotvar Bool) % 0.41/0.80 (declare-const tptp.laminj Bool) % 0.41/0.80 (declare-const tptp.axvarshift Bool) % 0.41/0.80 (declare-const tptp.ulamvarind Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 0.41/0.80 (declare-const tptp.ulamvarsh Bool) % 0.41/0.80 (declare-const tptp.ulamvar1 Bool) % 0.41/0.80 (declare-const tptp.axabs Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem1 Bool) % 0.41/0.80 (declare-const tptp.shinj Bool) % 0.41/0.80 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 0.41/0.80 (declare-const tptp.apinj2 Bool) % 0.41/0.80 (declare-const tptp.axvarid Bool) % 0.41/0.80 (declare-const tptp.axidl Bool) % 0.41/0.80 (declare-const tptp.axclos Bool) % 0.41/0.80 (declare-const tptp.termmset Bool) % 0.41/0.80 (declare-const tptp.axshiftcons Bool) % 0.41/0.80 (declare-const tptp.lamnotap Bool) % 0.41/0.80 (declare-const tptp.lamnotvar Bool) % 0.41/0.80 (declare-const tptp.axapp Bool) % 0.41/0.80 (declare-const tptp.axscons Bool) % 0.41/0.80 (declare-const tptp.axmap Bool) % 0.41/0.80 (declare-const tptp.axidr Bool) % 0.41/0.80 (declare-const tptp.induction2lem Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem1_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasapinj1_lthm Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem1_lthm Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem1v2 Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 0.41/0.80 (declare-const tptp.induction2 Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem2v2 Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem3v2 Bool) % 0.41/0.80 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 0.41/0.80 (declare-const tptp.pushprop Bool) % 0.41/0.80 (declare-const tptp.pushprop_gthm Bool) % 0.41/0.80 (declare-const tptp.hoasapinj1 Bool) % 0.41/0.80 (declare-const tptp.pushprop_lthm_orig Bool) % 0.41/0.80 (declare-const tptp.pushprop_lthm Bool) % 0.41/0.80 (declare-const tptp.induction2lem_gthm Bool) % 0.41/0.80 (declare-const tptp.induction2lem_lthm Bool) % 0.41/0.80 (declare-const tptp.induction2_gthm Bool) % 0.41/0.80 (declare-const tptp.induction2_lthm Bool) % 0.41/0.80 (declare-const tptp.substmonoid Bool) % 0.41/0.80 (declare-const tptp.substmonoid_gthm Bool) % 0.41/0.80 (declare-const tptp.termmset_gthm Bool) % 0.41/0.80 (declare-const tptp.substmonoid_lthm Bool) % 0.41/0.80 (declare-const tptp.termmset_lthm Bool) % 0.41/0.80 (declare-const tptp.hoasapinj1_gthm Bool) % 0.41/0.80 (define tptp.pushprop_p_and_p_prime () (let ((_let_1 (@var "M" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (let ((_let_3 (@var "X" tptp.term))) (let ((_let_4 (@var "P" (-> tptp.term Bool)))) (let ((_let_5 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_1 _let_4 _let_5) (forall (@list _let_3) (= (_ _let_5 _let_3) (_ _let_4 (_ (_ tptp.sub _let_3) (_ (_ tptp.push _let_2) _let_1)))))))))))) % 0.41/0.80 (define tptp.hoasap () (let ((_let_1 (@var "B" tptp.term))) (let ((_let_2 (@var "N" tptp.subst))) (let ((_let_3 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_3 _let_2 _let_1) (_ (_ tptp.ap (_ (_ tptp.sub _let_3) _let_2)) _let_1)))))) % 0.41/0.80 (define tptp.hoaslam () (let ((_let_1 (@var "F" (-> tptp.subst tptp.term tptp.term)))) (lambda (@list (@var "M" tptp.subst) _let_1) (_ tptp.lam (_ (_ _let_1 tptp.sh) tptp.one))))) % 0.41/0.80 (define tptp.hoasvar () (let ((_let_1 (@var "N" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_2 _let_1) (_ tptp.var (_ (_ tptp.sub _let_2) _let_1)))))) % 0.41/0.80 (define tptp.hoasinduction_p_and_p_prime () (let ((_let_1 (@var "X" tptp.term))) (let ((_let_2 (@var "P" (-> tptp.subst tptp.term tptp.subst Bool)))) (let ((_let_3 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (= (_ _let_3 _let_1) (_ (_ (_ _let_2 tptp.id) _let_1) tptp.id)))))))) % 0.41/0.80 (define @t1 () (@var "M" tptp.subst)) % 0.41/0.80 (define @t2 () (@var "B" tptp.term)) % 0.41/0.80 (define @t3 () (_ tptp.sub @t2)) % 0.41/0.80 (define @t4 () (_ @t3 @t1)) % 0.41/0.80 (define @t5 () (@var "A" tptp.term)) % 0.41/0.80 (define @t6 () (_ tptp.sub @t5)) % 0.41/0.80 (define @t7 () (_ @t6 @t1)) % 0.41/0.80 (define @t8 () (_ (_ tptp.ap @t7) @t4)) % 0.41/0.80 (define @t9 () (_ tptp.ap @t5)) % 0.41/0.80 (define @t10 () (_ @t9 @t2)) % 0.41/0.80 (define @t11 () (_ (_ tptp.sub @t10) @t1)) % 0.41/0.80 (define @t12 () (= @t11 @t8)) % 0.41/0.80 (define @t13 () (@list @t5 @t2 @t1)) % 0.41/0.80 (define @t14 () (forall @t13 @t12)) % 0.41/0.80 (define @t15 () (= tptp.axapp @t14)) % 0.41/0.80 (define @t16 () (_ (_ tptp.push @t5) @t1)) % 0.41/0.80 (define @t17 () (_ tptp.sub tptp.one)) % 0.41/0.80 (define @t18 () (_ @t17 @t16)) % 0.41/0.80 (define @t19 () (@list @t5 @t1)) % 0.41/0.80 (define @t20 () (forall @t19 (= @t18 @t5))) % 0.41/0.80 (define @t21 () (= tptp.axvarcons @t20)) % 0.41/0.80 (define @t22 () (_ @t6 tptp.id)) % 0.41/0.80 (define @t23 () (@list @t5)) % 0.41/0.80 (define @t24 () (forall @t23 (= @t22 @t5))) % 0.41/0.80 (define @t25 () (= tptp.axvarid @t24)) % 0.41/0.80 (define @t26 () (_ tptp.comp @t1)) % 0.41/0.80 (define @t27 () (_ @t26 tptp.sh)) % 0.41/0.80 (define @t28 () (_ tptp.push tptp.one)) % 0.41/0.80 (define @t29 () (_ @t28 @t27)) % 0.41/0.80 (define @t30 () (_ @t6 @t29)) % 0.41/0.80 (define @t31 () (_ tptp.lam @t30)) % 0.41/0.80 (define @t32 () (_ tptp.lam @t5)) % 0.41/0.80 (define @t33 () (_ (_ tptp.sub @t32) @t1)) % 0.41/0.80 (define @t34 () (= @t33 @t31)) % 0.41/0.80 (define @t35 () (forall @t19 @t34)) % 0.41/0.80 (define @t36 () (= tptp.axabs @t35)) % 0.41/0.80 (define @t37 () (@var "N" tptp.subst)) % 0.41/0.80 (define @t38 () (_ @t26 @t37)) % 0.41/0.80 (define @t39 () (_ @t6 @t38)) % 0.41/0.80 (define @t40 () (_ (_ tptp.sub @t7) @t37)) % 0.41/0.80 (define @t41 () (= @t40 @t39)) % 0.41/0.80 (define @t42 () (@list @t5 @t1 @t37)) % 0.41/0.80 (define @t43 () (forall @t42 @t41)) % 0.41/0.80 (define @t44 () (= tptp.axclos @t43)) % 0.41/0.80 (define @t45 () (_ (_ tptp.comp tptp.id) @t1)) % 0.41/0.80 (define @t46 () (@list @t1)) % 0.41/0.80 (define @t47 () (forall @t46 (= @t45 @t1))) % 0.41/0.80 (define @t48 () (= tptp.axidl @t47)) % 0.41/0.80 (define @t49 () (_ tptp.comp tptp.sh)) % 0.41/0.80 (define @t50 () (_ @t49 @t16)) % 0.41/0.80 (define @t51 () (forall @t19 (= @t50 @t1))) % 0.41/0.80 (define @t52 () (= tptp.axshiftcons @t51)) % 0.41/0.80 (define @t53 () (@var "K" tptp.subst)) % 0.41/0.80 (define @t54 () (_ (_ tptp.comp @t37) @t53)) % 0.41/0.80 (define @t55 () (_ @t26 @t54)) % 0.41/0.80 (define @t56 () (_ (_ tptp.comp @t38) @t53)) % 0.41/0.80 (define @t57 () (= @t56 @t55)) % 0.41/0.80 (define @t58 () (@list @t1 @t37 @t53)) % 0.41/0.80 (define @t59 () (forall @t58 @t57)) % 0.41/0.80 (define @t60 () (= tptp.axassoc @t59)) % 0.41/0.80 (define @t61 () (_ @t6 @t37)) % 0.41/0.80 (define @t62 () (_ (_ tptp.push @t61) @t38)) % 0.41/0.80 (define @t63 () (_ (_ tptp.comp @t16) @t37)) % 0.41/0.80 (define @t64 () (= @t63 @t62)) % 0.41/0.80 (define @t65 () (forall @t42 @t64)) % 0.41/0.80 (define @t66 () (= tptp.axmap @t65)) % 0.41/0.80 (define @t67 () (_ @t26 tptp.id)) % 0.41/0.80 (define @t68 () (forall @t46 (= @t67 @t1))) % 0.41/0.80 (define @t69 () (= tptp.axidr @t68)) % 0.41/0.80 (define @t70 () (_ @t28 tptp.sh)) % 0.41/0.80 (define @t71 () (= tptp.axvarshift (= @t70 tptp.id))) % 0.41/0.80 (define @t72 () (_ @t49 @t1)) % 0.41/0.80 (define @t73 () (_ @t17 @t1)) % 0.41/0.80 (define @t74 () (_ (_ tptp.push @t73) @t72)) % 0.41/0.80 (define @t75 () (forall @t46 (= @t74 @t1))) % 0.41/0.80 (define @t76 () (= tptp.axscons @t75)) % 0.41/0.80 (define @t77 () (_ tptp.var tptp.one)) % 0.41/0.80 (define @t78 () (_ @t6 tptp.sh)) % 0.41/0.80 (define @t79 () (_ tptp.var @t78)) % 0.41/0.80 (define @t80 () (_ tptp.var @t5)) % 0.41/0.80 (define @t81 () (forall @t23 (=> @t80 @t79))) % 0.41/0.80 (define @t82 () (= tptp.ulamvarsh @t81)) % 0.41/0.80 (define @t83 () (@var "P" (-> tptp.term Bool))) % 0.41/0.80 (define @t84 () (_ @t83 @t5)) % 0.41/0.80 (define @t85 () (forall @t23 (=> @t80 @t84))) % 0.41/0.80 (define @t86 () (_ @t83 @t78)) % 0.41/0.80 (define @t87 () (=> @t84 @t86)) % 0.41/0.80 (define @t88 () (forall @t23 (=> @t80 @t87))) % 0.41/0.80 (define @t89 () (=> @t88 @t85)) % 0.41/0.80 (define @t90 () (_ @t83 tptp.one)) % 0.41/0.80 (define @t91 () (=> @t90 @t89)) % 0.41/0.80 (define @t92 () (@list @t83)) % 0.41/0.80 (define @t93 () (forall @t92 @t91)) % 0.41/0.80 (define @t94 () (= tptp.ulamvarind @t93)) % 0.41/0.80 (define @t95 () (= @t5 @t2)) % 0.41/0.80 (define @t96 () (@var "D" tptp.term)) % 0.41/0.80 (define @t97 () (_ tptp.ap @t2)) % 0.41/0.80 (define @t98 () (_ @t97 @t96)) % 0.41/0.80 (define @t99 () (@var "C" tptp.term)) % 0.41/0.80 (define @t100 () (_ @t9 @t99)) % 0.41/0.80 (define @t101 () (= @t100 @t98)) % 0.41/0.80 (define @t102 () (@list @t5 @t2 @t99 @t96)) % 0.41/0.80 (define @t103 () (forall @t102 (=> @t101 @t95))) % 0.41/0.80 (define @t104 () (= tptp.apinj1 @t103)) % 0.41/0.80 (define @t105 () (= @t99 @t96)) % 0.41/0.80 (define @t106 () (forall @t102 (=> @t101 @t105))) % 0.41/0.80 (define @t107 () (= tptp.apinj2 @t106)) % 0.41/0.80 (define @t108 () (_ tptp.lam @t2)) % 0.41/0.80 (define @t109 () (= @t32 @t108)) % 0.41/0.80 (define @t110 () (@list @t5 @t2)) % 0.41/0.80 (define @t111 () (forall @t110 (=> @t109 @t95))) % 0.41/0.80 (define @t112 () (= tptp.laminj @t111)) % 0.41/0.80 (define @t113 () (_ @t3 tptp.sh)) % 0.41/0.80 (define @t114 () (= @t78 @t113)) % 0.41/0.80 (define @t115 () (forall @t110 (=> @t114 @t95))) % 0.41/0.80 (define @t116 () (= tptp.shinj @t115)) % 0.41/0.80 (define @t117 () (_ @t97 @t99)) % 0.41/0.80 (define @t118 () (= @t32 @t117)) % 0.41/0.80 (define @t119 () (not @t118)) % 0.41/0.80 (define @t120 () (@list @t5 @t2 @t99)) % 0.41/0.80 (define @t121 () (forall @t120 @t119)) % 0.41/0.80 (define @t122 () (= tptp.lamnotap @t121)) % 0.41/0.80 (define @t123 () (_ tptp.var @t10)) % 0.41/0.80 (define @t124 () (not @t123)) % 0.41/0.80 (define @t125 () (forall @t110 @t124)) % 0.41/0.80 (define @t126 () (= tptp.apnotvar @t125)) % 0.41/0.80 (define @t127 () (_ tptp.var @t32)) % 0.41/0.80 (define @t128 () (not @t127)) % 0.41/0.80 (define @t129 () (forall @t23 @t128)) % 0.41/0.80 (define @t130 () (= tptp.lamnotvar @t129)) % 0.41/0.80 (define @t131 () (forall @t23 @t84)) % 0.41/0.80 (define @t132 () (_ @t83 @t32)) % 0.41/0.80 (define @t133 () (forall @t23 (=> @t84 @t132))) % 0.41/0.80 (define @t134 () (=> @t133 @t131)) % 0.41/0.80 (define @t135 () (_ @t83 @t10)) % 0.41/0.80 (define @t136 () (_ @t83 @t2)) % 0.41/0.80 (define @t137 () (=> @t136 @t135)) % 0.41/0.80 (define @t138 () (forall @t110 (=> @t84 @t137))) % 0.41/0.80 (define @t139 () (=> @t138 @t134)) % 0.41/0.80 (define @t140 () (=> @t85 @t139)) % 0.41/0.80 (define @t141 () (forall @t92 @t140)) % 0.41/0.80 (define @t142 () (= tptp.induction @t141)) % 0.41/0.80 (define @t143 () (@var "Q" (-> tptp.term Bool))) % 0.41/0.80 (define @t144 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t83) @t143)) % 0.41/0.80 (define @t145 () (@list @t143)) % 0.41/0.80 (define @t146 () (@list @t83 @t5 @t1)) % 0.41/0.80 (define @t147 () (_ tptp.push @t2)) % 0.41/0.80 (define @t148 () (@var "K" (-> tptp.term Bool))) % 0.41/0.80 (define @t149 () (@list @t83 @t143 @t5 @t1)) % 0.41/0.80 (define @t150 () (_ tptp.sub @t99)) % 0.41/0.81 (define @t151 () (@list @t99)) % 0.41/0.81 (define @t152 () (_ @t83 @t4)) % 0.41/0.81 (define @t153 () (_ tptp.var @t2)) % 0.41/0.81 (define @t154 () (@list @t2)) % 0.41/0.81 (define @t155 () (forall @t154 (=> @t153 @t152))) % 0.41/0.81 (define @t156 () (_ @t3 @t16)) % 0.41/0.81 (define @t157 () (_ @t83 @t156)) % 0.41/0.81 (define @t158 () (forall @t154 (=> @t153 @t157))) % 0.41/0.81 (define @t159 () (_ @t143 @t2)) % 0.41/0.81 (define @t160 () (=> @t84 @t158)) % 0.41/0.81 (define @t161 () (=> @t155 @t160)) % 0.41/0.81 (define @t162 () (forall @t146 @t161)) % 0.41/0.81 (define @t163 () (= tptp.pushprop @t162)) % 0.41/0.81 (define @t164 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 0.41/0.81 (define @t165 () (_ @t83 @t7)) % 0.41/0.81 (define @t166 () (=> @t155 @t165)) % 0.41/0.81 (define @t167 () (forall @t19 @t166)) % 0.41/0.81 (define @t168 () (_ @t147 tptp.id)) % 0.41/0.81 (define @t169 () (_ @t6 @t168)) % 0.41/0.81 (define @t170 () (_ @t83 @t169)) % 0.41/0.81 (define @t171 () (forall @t154 (=> @t136 @t170))) % 0.41/0.81 (define @t172 () (=> @t171 @t132)) % 0.41/0.81 (define @t173 () (forall @t23 @t172)) % 0.41/0.81 (define @t174 () (=> @t173 @t167)) % 0.41/0.81 (define @t175 () (=> @t138 @t174)) % 0.41/0.81 (define @t176 () (forall @t92 @t175)) % 0.41/0.81 (define @t177 () (= tptp.induction2lem @t176)) % 0.41/0.81 (define @t178 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 0.41/0.81 (define @t179 () (=> @t173 @t131)) % 0.41/0.81 (define @t180 () (=> @t138 @t179)) % 0.41/0.81 (define @t181 () (=> @t85 @t180)) % 0.41/0.81 (define @t182 () (forall @t92 @t181)) % 0.41/0.81 (define @t183 () (= tptp.induction2 @t182)) % 0.41/0.81 (define @t184 () (=> tptp.induction2lem tptp.induction2)) % 0.41/0.81 (define @t185 () (and @t59 @t47 @t68)) % 0.41/0.81 (define @t186 () (= tptp.substmonoid @t185)) % 0.41/0.81 (define @t187 () (and @t43 @t24)) % 0.41/0.81 (define @t188 () (= tptp.termmset @t187)) % 0.41/0.81 (define @t189 () (_ tptp.hoasap tptp.id)) % 0.41/0.81 (define @t190 () (_ (_ @t189 @t5) tptp.id)) % 0.41/0.81 (define @t191 () (= (_ @t190 @t99) (_ (_ (_ @t189 @t2) tptp.id) @t96))) % 0.41/0.81 (define @t192 () (=> @t191 @t95)) % 0.41/0.81 (define @t193 () (forall @t102 @t192)) % 0.41/0.81 (define @t194 () (= tptp.hoasapinj1 @t193)) % 0.41/0.81 (define @t195 () (=> @t191 @t105)) % 0.41/0.81 (define @t196 () (forall @t102 @t195)) % 0.41/0.81 (define @t197 () (= tptp.hoasapinj2 @t196)) % 0.41/0.81 (define @t198 () (=> tptp.hoasapinj1 tptp.hoasapinj2)) % 0.41/0.81 (define @t199 () (=> tptp.termmset @t198)) % 0.41/0.81 (define @t200 () (=> tptp.substmonoid @t199)) % 0.41/0.81 (define @t201 () (=> tptp.induction2 @t200)) % 0.41/0.81 (define @t202 () (=> tptp.induction2lem @t201)) % 0.41/0.81 (define @t203 () (=> tptp.pushprop @t202)) % 0.41/0.81 (define @t204 () (=> tptp.induction @t203)) % 0.41/0.81 (define @t205 () (=> tptp.lamnotvar @t204)) % 0.41/0.81 (define @t206 () (=> tptp.apnotvar @t205)) % 0.41/0.81 (define @t207 () (=> tptp.lamnotap @t206)) % 0.41/0.81 (define @t208 () (=> tptp.shinj @t207)) % 0.41/0.81 (define @t209 () (=> tptp.laminj @t208)) % 0.41/0.81 (define @t210 () (=> tptp.apinj2 @t209)) % 0.41/0.81 (define @t211 () (=> tptp.apinj1 @t210)) % 0.41/0.81 (define @t212 () (=> tptp.ulamvarind @t211)) % 0.41/0.81 (define @t213 () (=> tptp.ulamvarsh @t212)) % 0.41/0.81 (define @t214 () (=> tptp.ulamvar1 @t213)) % 0.41/0.81 (define @t215 () (=> tptp.axscons @t214)) % 0.41/0.81 (define @t216 () (=> tptp.axvarshift @t215)) % 0.41/0.81 (define @t217 () (=> tptp.axidr @t216)) % 0.41/0.81 (define @t218 () (=> tptp.axmap @t217)) % 0.41/0.81 (define @t219 () (=> tptp.axassoc @t218)) % 0.41/0.81 (define @t220 () (=> tptp.axshiftcons @t219)) % 0.41/0.81 (define @t221 () (=> tptp.axidl @t220)) % 0.41/0.81 (define @t222 () (=> tptp.axclos @t221)) % 0.41/0.81 (define @t223 () (=> tptp.axabs @t222)) % 0.41/0.81 (define @t224 () (=> tptp.axvarid @t223)) % 0.41/0.81 (define @t225 () (=> tptp.axvarcons @t224)) % 0.41/0.81 (define @t226 () (=> tptp.axapp @t225)) % 0.41/0.81 (define @t227 () (= tptp.hoasapinj2_gthm @t226)) % 0.41/0.81 (define @t228 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.81 (define @t229 () (_ (_ @t228 @t1) @t5)) % 0.41/0.81 (define @t230 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 0.41/0.81 (define @t231 () (_ @t230 @t1)) % 0.41/0.81 (define @t232 () (_ @t231 @t5)) % 0.41/0.81 (define @t233 () (@list @t1 @t5)) % 0.41/0.81 (define @t234 () (_ tptp.hoaslam tptp.id)) % 0.41/0.81 (define @t235 () (_ @t234 (lambda @t233 @t232))) % 0.41/0.81 (define @t236 () (@list @t1 @t5 @t37)) % 0.41/0.81 (define @t237 () (_ (_ @t230 @t38) @t61)) % 0.41/0.81 (define @t238 () (_ (_ tptp.sub @t232) @t37)) % 0.41/0.81 (define @t239 () (forall @t236 (= @t238 @t237))) % 0.41/0.81 (define @t240 () (@list @t230)) % 0.41/0.81 (define @t241 () (_ @t190 @t2)) % 0.41/0.81 (define @t242 () (_ tptp.hoasvar tptp.id)) % 0.41/0.81 (define @t243 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 0.41/0.81 (define @t244 () (_ (_ tptp.hoasinduction_p_and_p_prime @t243) @t143)) % 0.41/0.81 (define @t245 () (@list @t243)) % 0.41/0.81 (define @t246 () (_ @t143 @t5)) % 0.41/0.81 (define @t247 () (_ @t243 tptp.id)) % 0.41/0.81 (define @t248 () (_ (_ @t247 @t5) tptp.id)) % 0.41/0.81 (define @t249 () (forall @t23 (=> (_ (_ @t242 @t5) tptp.id) @t248))) % 0.41/0.81 (define @t250 () (_ (_ (_ @t243 @t1) @t5) (_ (_ tptp.comp @t53) @t37))) % 0.41/0.81 (define @t251 () (_ (_ (_ @t243 (_ @t26 @t53)) (_ @t6 @t53)) @t37)) % 0.41/0.81 (define @t252 () (@list @t1 @t5 @t37 @t53)) % 0.41/0.81 (define @t253 () (forall @t252 (=> @t251 @t250))) % 0.41/0.81 (define @t254 () (forall @t252 (=> @t250 @t251))) % 0.41/0.81 (define @t255 () (@list @t243 @t143)) % 0.41/0.81 (define @t256 () (_ (_ @t247 @t2) tptp.id)) % 0.41/0.81 (define @t257 () (forall @t110 (=> @t248 (=> @t256 (_ (_ @t247 @t241) tptp.id))))) % 0.41/0.81 (define @t258 () (=> (forall @t23 (=> @t248 (_ (_ @t247 (_ (_ @t230 tptp.id) @t5)) tptp.id))) (_ (_ @t247 @t235) tptp.id))) % 0.41/0.81 (define @t259 () (forall @t240 (=> @t239 @t258))) % 0.41/0.81 (define @t260 () (=> @t259 (=> @t244 (forall @t23 (=> (forall @t154 (=> @t159 (_ @t143 @t169))) (_ @t143 @t32)))))) % 0.41/0.81 (define @t261 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1))))))))))))))))))))))))))))))))))) % 0.41/0.81 (define @t262 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2))))))))))))))))))))))))))))))))))) % 0.41/0.81 (define @t263 () (forall @t154 (=> @t256 (_ (_ @t247 @t169) tptp.id)))) % 0.41/0.81 (define @t264 () (forall @t23 (=> @t263 (_ (_ @t247 (_ tptp.lam (_ @t6 @t70))) tptp.id)))) % 0.41/0.81 (define @t265 () (=> @t259 (forall @t23 (=> @t263 (_ (_ @t247 @t32) tptp.id))))) % 0.41/0.81 (define @t266 () (_ (_ @t230 tptp.sh) tptp.one)) % 0.41/0.81 (define @t267 () (=> @t257 (=> @t259 (forall @t23 @t248)))) % 0.41/0.81 (define @t268 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 0.41/0.81 (define @t269 () (not tptp.hoasapinj2_gthm)) % 0.41/0.81 (define @t270 () (@var "X" tptp.term)) % 0.41/0.81 (define @t271 () (_ @t143 @t270)) % 0.41/0.81 (define @t272 () (@list @t270)) % 0.41/0.81 (define @t273 () (lambda (@list @t5 @t1 @t83 @t143) (forall @t272 (= @t271 (_ @t83 (_ (_ tptp.sub @t270) @t16)))))) % 0.41/0.81 (define @t274 () (_ tptp.ap @t61)) % 0.41/0.81 (define @t275 () (_ @t274 @t2)) % 0.41/0.81 (define @t276 () (lambda (@list @t1 @t5 @t37 @t2) @t275)) % 0.41/0.81 (define @t277 () (lambda (@list @t1 @t230) (_ tptp.lam @t266))) % 0.41/0.81 (define @t278 () (lambda @t236 (_ tptp.var @t61))) % 0.41/0.81 (define @t279 () (lambda @t255 (forall @t272 (= @t271 (_ (_ @t247 @t270) tptp.id))))) % 0.41/0.81 (define @t280 () (tptp.push tptp.one tptp.sh)) % 0.41/0.81 (define @t281 () (tptp.sub @t5 @t280)) % 0.41/0.81 (define @t282 () (not (= (tptp.ap (tptp.sub @t2 @t280) @t96) (tptp.ap @t281 @t99)))) % 0.41/0.81 (define @t283 () (forall @t102 (or @t282 @t105))) % 0.41/0.81 (define @t284 () (forall @t23 (= @t5 @t281))) % 0.41/0.81 (define @t285 () (tptp.comp @t1 @t37)) % 0.41/0.81 (define @t286 () (tptp.sub @t5 @t285)) % 0.41/0.81 (define @t287 () (tptp.sub @t5 @t1)) % 0.41/0.81 (define @t288 () (tptp.sub @t287 @t37)) % 0.41/0.81 (define @t289 () (forall @t42 (= @t288 @t286))) % 0.41/0.81 (define @t290 () (forall @t46 (= @t1 (tptp.comp @t1 @t280)))) % 0.41/0.81 (define @t291 () (forall @t46 (= @t1 (tptp.comp @t280 @t1)))) % 0.41/0.81 (define @t292 () (tptp.comp @t37 @t53)) % 0.41/0.81 (define @t293 () (tptp.comp @t1 @t292)) % 0.41/0.81 (define @t294 () (tptp.comp @t285 @t53)) % 0.41/0.81 (define @t295 () (forall @t58 (= @t294 @t293))) % 0.41/0.81 (define @t296 () (@var "BOUND_VARIABLE_9396" tptp.term)) % 0.41/0.81 (define @t297 () (_ @t83 @t296)) % 0.41/0.81 (define @t298 () (tptp.lam @t5)) % 0.41/0.81 (define @t299 () (_ @t83 @t298)) % 0.41/0.81 (define @t300 () (_ @t83 @t2)) % 0.41/0.81 (define @t301 () (not @t300)) % 0.41/0.81 (define @t302 () (not (forall @t23 (or (not (forall @t154 (or @t301 (_ @t83 (tptp.sub @t5 (tptp.push @t2 @t280)))))) @t299)))) % 0.41/0.81 (define @t303 () (tptp.ap @t5 @t2)) % 0.41/0.81 (define @t304 () (_ @t83 @t303)) % 0.41/0.81 (define @t305 () (_ @t83 @t5)) % 0.41/0.81 (define @t306 () (not @t305)) % 0.41/0.81 (define @t307 () (forall @t110 (or @t306 @t301 @t304))) % 0.41/0.81 (define @t308 () (not @t307)) % 0.41/0.81 (define @t309 () (tptp.var @t5)) % 0.41/0.81 (define @t310 () (not @t309)) % 0.41/0.81 (define @t311 () (forall @t23 (or @t310 @t305))) % 0.41/0.81 (define @t312 () (not @t311)) % 0.41/0.81 (define @t313 () (@list @t83 @t296)) % 0.41/0.81 (define @t314 () (@var "BOUND_VARIABLE_9371" tptp.subst)) % 0.41/0.81 (define @t315 () (@var "BOUND_VARIABLE_9369" tptp.term)) % 0.41/0.81 (define @t316 () (_ @t83 (tptp.sub @t315 @t314))) % 0.41/0.81 (define @t317 () (tptp.var @t2)) % 0.41/0.81 (define @t318 () (not @t317)) % 0.41/0.81 (define @t319 () (not (forall @t154 (or @t318 (_ @t83 (tptp.sub @t2 @t314)))))) % 0.41/0.81 (define @t320 () (@list @t83 @t315 @t314)) % 0.41/0.81 (define @t321 () (tptp.push @t5 @t1)) % 0.41/0.81 (define @t322 () (@var "BOUND_VARIABLE_9324" tptp.term)) % 0.41/0.81 (define @t323 () (_ @t83 (tptp.sub @t322 @t321))) % 0.41/0.81 (define @t324 () (not (tptp.var @t322))) % 0.41/0.81 (define @t325 () (tptp.sub @t2 @t1)) % 0.41/0.81 (define @t326 () (_ @t83 @t325)) % 0.41/0.81 (define @t327 () (forall @t154 (or @t318 @t326))) % 0.41/0.81 (define @t328 () (not @t327)) % 0.41/0.81 (define @t329 () (or @t328 @t306 @t324 @t323)) % 0.41/0.81 (define @t330 () (@list @t83 @t5 @t1 @t322)) % 0.41/0.81 (define @t331 () (forall @t330 @t329)) % 0.41/0.81 (define @t332 () (@var "BOUND_VARIABLE_9170" tptp.term)) % 0.41/0.81 (define @t333 () (_ @t83 @t332)) % 0.41/0.81 (define @t334 () (forall @t23 (or @t306 @t299))) % 0.41/0.81 (define @t335 () (not @t334)) % 0.41/0.81 (define @t336 () (or @t312 @t308 @t335 @t333)) % 0.41/0.81 (define @t337 () (forall (@list @t83 @t332) @t336)) % 0.41/0.81 (define @t338 () (tptp.var @t298)) % 0.41/0.81 (define @t339 () (forall @t23 (not @t338))) % 0.41/0.81 (define @t340 () (tptp.var @t303)) % 0.41/0.81 (define @t341 () (forall @t110 (not @t340))) % 0.41/0.81 (define @t342 () (tptp.ap @t2 @t99)) % 0.41/0.81 (define @t343 () (forall @t120 (not (= @t298 @t342)))) % 0.41/0.81 (define @t344 () (tptp.sub @t2 tptp.sh)) % 0.41/0.81 (define @t345 () (tptp.sub @t5 tptp.sh)) % 0.41/0.81 (define @t346 () (forall @t110 (or (not (= @t345 @t344)) @t95))) % 0.41/0.81 (define @t347 () (tptp.lam @t2)) % 0.41/0.81 (define @t348 () (forall @t110 (or (not (= @t298 @t347)) @t95))) % 0.41/0.81 (define @t349 () (tptp.ap @t2 @t96)) % 0.41/0.81 (define @t350 () (tptp.ap @t5 @t99)) % 0.41/0.81 (define @t351 () (not (= @t350 @t349))) % 0.41/0.81 (define @t352 () (forall @t102 (or @t351 @t105))) % 0.41/0.81 (define @t353 () (forall @t102 (or @t351 @t95))) % 0.41/0.81 (define @t354 () (@var "BOUND_VARIABLE_9074" tptp.term)) % 0.41/0.81 (define @t355 () (_ @t83 @t354)) % 0.41/0.81 (define @t356 () (not (tptp.var @t354))) % 0.41/0.81 (define @t357 () (_ @t83 @t345)) % 0.41/0.81 (define @t358 () (forall @t23 (or @t310 @t306 @t357))) % 0.41/0.81 (define @t359 () (not @t358)) % 0.41/0.81 (define @t360 () (_ @t83 tptp.one)) % 0.41/0.81 (define @t361 () (not @t360)) % 0.41/0.81 (define @t362 () (or @t361 @t359 @t356 @t355)) % 0.41/0.81 (define @t363 () (@list @t83 @t354)) % 0.41/0.81 (define @t364 () (forall @t363 @t362)) % 0.41/0.81 (define @t365 () (tptp.var @t345)) % 0.41/0.81 (define @t366 () (forall @t23 (or @t310 @t365))) % 0.41/0.81 (define @t367 () (=> @t366 (=> @t364 (=> @t353 (=> @t352 (=> @t348 (=> @t346 (=> @t343 (=> @t341 (=> @t339 (=> @t337 (=> @t331 (=> (forall @t320 (or @t308 @t302 @t319 @t316)) (=> (forall @t313 (or @t312 @t308 @t302 @t297)) (=> (and @t295 @t291 @t290) (=> (and @t289 @t284) (=> (forall @t102 (or @t282 @t95)) @t283))))))))))))))))) % 0.41/0.81 (define @t368 () (tptp.var tptp.one)) % 0.41/0.81 (define @t369 () (=> @t77 @t367)) % 0.41/0.81 (define @t370 () (tptp.comp tptp.sh @t1)) % 0.41/0.81 (define @t371 () (tptp.sub tptp.one @t1)) % 0.41/0.81 (define @t372 () (tptp.push @t371 @t370)) % 0.41/0.81 (define @t373 () (forall @t46 (= @t1 @t372))) % 0.41/0.81 (define @t374 () (=> @t373 @t369)) % 0.41/0.81 (define @t375 () (=> @t290 @t374)) % 0.41/0.81 (define @t376 () (tptp.sub @t5 @t37)) % 0.41/0.81 (define @t377 () (tptp.push @t376 @t285)) % 0.41/0.81 (define @t378 () (tptp.comp @t321 @t37)) % 0.41/0.81 (define @t379 () (forall @t42 (= @t378 @t377))) % 0.41/0.81 (define @t380 () (=> @t379 @t375)) % 0.41/0.81 (define @t381 () (=> @t295 @t380)) % 0.41/0.81 (define @t382 () (tptp.comp tptp.sh @t321)) % 0.41/0.81 (define @t383 () (forall @t19 (= @t1 @t382))) % 0.41/0.81 (define @t384 () (=> @t383 @t381)) % 0.41/0.81 (define @t385 () (=> @t291 @t384)) % 0.41/0.81 (define @t386 () (=> @t289 @t385)) % 0.41/0.81 (define @t387 () (tptp.comp @t1 tptp.sh)) % 0.41/0.81 (define @t388 () (tptp.push tptp.one @t387)) % 0.41/0.81 (define @t389 () (tptp.sub @t5 @t388)) % 0.41/0.81 (define @t390 () (tptp.lam @t389)) % 0.41/0.81 (define @t391 () (tptp.sub @t298 @t1)) % 0.41/0.81 (define @t392 () (forall @t19 (= @t391 @t390))) % 0.41/0.81 (define @t393 () (=> @t392 @t386)) % 0.41/0.81 (define @t394 () (=> @t284 @t393)) % 0.41/0.81 (define @t395 () (tptp.sub tptp.one @t321)) % 0.41/0.81 (define @t396 () (forall @t19 (= @t5 @t395))) % 0.41/0.81 (define @t397 () (=> @t396 @t394)) % 0.41/0.81 (define @t398 () (tptp.ap @t287 @t325)) % 0.41/0.81 (define @t399 () (tptp.sub @t303 @t1)) % 0.41/0.81 (define @t400 () (forall @t13 (= @t399 @t398))) % 0.41/0.81 (define @t401 () (=> @t400 @t397)) % 0.41/0.81 (define @t402 () (tptp.sub @t5 @t70)) % 0.41/0.81 (define @t403 () (tptp.ap @t402 @t99)) % 0.41/0.81 (define @t404 () (tptp.sub @t2 @t70)) % 0.41/0.81 (define @t405 () (tptp.ap @t404 @t96)) % 0.41/0.81 (define @t406 () (= @t405 @t403)) % 0.41/0.81 (define @t407 () (not @t406)) % 0.41/0.81 (define @t408 () (or @t407 @t105)) % 0.41/0.81 (define @t409 () (not (= @t403 @t405))) % 0.41/0.81 (define @t410 () (or @t409 @t105)) % 0.41/0.81 (define @t411 () (forall @t102 @t410)) % 0.41/0.81 (define @t412 () (or @t407 @t95)) % 0.41/0.81 (define @t413 () (or @t409 @t95)) % 0.41/0.81 (define @t414 () (forall @t102 @t413)) % 0.41/0.81 (define @t415 () (=> @t414 @t411)) % 0.41/0.81 (define @t416 () (= @t5 @t402)) % 0.41/0.81 (define @t417 () (forall @t23 @t416)) % 0.41/0.81 (define @t418 () (and @t289 @t417)) % 0.41/0.81 (define @t419 () (=> @t418 @t415)) % 0.41/0.81 (define @t420 () (tptp.comp @t1 @t70)) % 0.41/0.81 (define @t421 () (= @t1 @t420)) % 0.41/0.81 (define @t422 () (forall @t46 @t421)) % 0.41/0.81 (define @t423 () (tptp.comp @t70 @t1)) % 0.41/0.81 (define @t424 () (= @t1 @t423)) % 0.41/0.81 (define @t425 () (forall @t46 @t424)) % 0.41/0.81 (define @t426 () (and @t295 @t425 @t422)) % 0.41/0.81 (define @t427 () (=> @t426 @t419)) % 0.41/0.81 (define @t428 () (tptp.push @t2 @t70)) % 0.41/0.81 (define @t429 () (tptp.sub @t5 @t428)) % 0.41/0.81 (define @t430 () (_ @t83 @t429)) % 0.41/0.81 (define @t431 () (or @t301 @t430)) % 0.41/0.81 (define @t432 () (forall @t154 @t431)) % 0.41/0.81 (define @t433 () (not @t432)) % 0.41/0.81 (define @t434 () (or @t433 @t299)) % 0.41/0.81 (define @t435 () (forall @t23 @t434)) % 0.41/0.81 (define @t436 () (not @t435)) % 0.41/0.81 (define @t437 () (or @t312 @t308 @t436 @t297)) % 0.41/0.81 (define @t438 () (forall @t313 @t437)) % 0.41/0.81 (define @t439 () (=> @t438 @t427)) % 0.41/0.81 (define @t440 () (or @t308 @t436 @t319 @t316)) % 0.41/0.81 (define @t441 () (forall @t320 @t440)) % 0.41/0.81 (define @t442 () (=> @t441 @t439)) % 0.41/0.81 (define @t443 () (=> @t331 @t442)) % 0.41/0.81 (define @t444 () (=> @t337 @t443)) % 0.41/0.81 (define @t445 () (=> @t339 @t444)) % 0.41/0.81 (define @t446 () (=> @t341 @t445)) % 0.41/0.81 (define @t447 () (=> @t343 @t446)) % 0.41/0.81 (define @t448 () (=> @t346 @t447)) % 0.41/0.81 (define @t449 () (=> @t348 @t448)) % 0.41/0.81 (define @t450 () (=> @t352 @t449)) % 0.41/0.81 (define @t451 () (=> @t353 @t450)) % 0.41/0.81 (define @t452 () (=> @t364 @t451)) % 0.41/0.81 (define @t453 () (=> @t366 @t452)) % 0.41/0.81 (define @t454 () (=> @t77 @t453)) % 0.41/0.81 (define @t455 () (=> @t373 @t454)) % 0.41/0.81 (define @t456 () (=> (= @t70 @t70) @t455)) % 0.41/0.81 (define @t457 () (=> @t422 @t456)) % 0.41/0.81 (define @t458 () (=> @t379 @t457)) % 0.41/0.81 (define @t459 () (=> @t295 @t458)) % 0.41/0.81 (define @t460 () (=> @t383 @t459)) % 0.41/0.81 (define @t461 () (=> @t425 @t460)) % 0.41/0.81 (define @t462 () (=> @t289 @t461)) % 0.41/0.81 (define @t463 () (=> @t392 @t462)) % 0.41/0.81 (define @t464 () (=> @t417 @t463)) % 0.41/0.81 (define @t465 () (=> @t396 @t464)) % 0.41/0.81 (define @t466 () (=> @t400 @t465)) % 0.41/0.81 (define @t467 () (tptp.sub @t2 tptp.id)) % 0.41/0.81 (define @t468 () (tptp.ap @t467 @t96)) % 0.41/0.81 (define @t469 () (tptp.sub @t5 tptp.id)) % 0.41/0.81 (define @t470 () (tptp.ap @t469 @t99)) % 0.41/0.81 (define @t471 () (= @t470 @t468)) % 0.41/0.81 (define @t472 () (not @t471)) % 0.41/0.81 (define @t473 () (or @t472 @t105)) % 0.41/0.81 (define @t474 () (forall @t102 @t473)) % 0.41/0.81 (define @t475 () (or @t472 @t95)) % 0.41/0.81 (define @t476 () (forall @t102 @t475)) % 0.41/0.81 (define @t477 () (=> @t476 @t474)) % 0.41/0.81 (define @t478 () (= @t5 @t469)) % 0.41/0.81 (define @t479 () (forall @t23 @t478)) % 0.41/0.81 (define @t480 () (and @t289 @t479)) % 0.41/0.81 (define @t481 () (=> @t480 @t477)) % 0.41/0.81 (define @t482 () (tptp.comp @t1 tptp.id)) % 0.41/0.81 (define @t483 () (= @t1 @t482)) % 0.41/0.81 (define @t484 () (forall @t46 @t483)) % 0.41/0.81 (define @t485 () (tptp.comp tptp.id @t1)) % 0.41/0.81 (define @t486 () (= @t1 @t485)) % 0.41/0.81 (define @t487 () (forall @t46 @t486)) % 0.41/0.81 (define @t488 () (and @t295 @t487 @t484)) % 0.41/0.81 (define @t489 () (=> @t488 @t481)) % 0.41/0.81 (define @t490 () (tptp.push @t2 tptp.id)) % 0.41/0.81 (define @t491 () (tptp.sub @t5 @t490)) % 0.41/0.81 (define @t492 () (_ @t83 @t491)) % 0.41/0.81 (define @t493 () (or @t301 @t492)) % 0.41/0.81 (define @t494 () (forall @t154 @t493)) % 0.41/0.81 (define @t495 () (not @t494)) % 0.41/0.81 (define @t496 () (or @t495 @t299)) % 0.41/0.81 (define @t497 () (forall @t23 @t496)) % 0.41/0.81 (define @t498 () (not @t497)) % 0.41/0.81 (define @t499 () (or @t312 @t308 @t498 @t297)) % 0.41/0.81 (define @t500 () (forall @t313 @t499)) % 0.41/0.81 (define @t501 () (=> @t500 @t489)) % 0.41/0.81 (define @t502 () (or @t308 @t498 @t319 @t316)) % 0.41/0.81 (define @t503 () (forall @t320 @t502)) % 0.41/0.81 (define @t504 () (=> @t503 @t501)) % 0.41/0.81 (define @t505 () (=> @t331 @t504)) % 0.41/0.81 (define @t506 () (=> @t337 @t505)) % 0.41/0.81 (define @t507 () (=> @t339 @t506)) % 0.41/0.81 (define @t508 () (=> @t341 @t507)) % 0.41/0.81 (define @t509 () (=> @t343 @t508)) % 0.41/0.81 (define @t510 () (=> @t346 @t509)) % 0.41/0.81 (define @t511 () (=> @t348 @t510)) % 0.41/0.81 (define @t512 () (=> @t352 @t511)) % 0.41/0.81 (define @t513 () (=> @t353 @t512)) % 0.41/0.81 (define @t514 () (=> @t364 @t513)) % 0.41/0.81 (define @t515 () (=> @t366 @t514)) % 0.41/0.81 (define @t516 () (=> @t77 @t515)) % 0.41/0.81 (define @t517 () (=> @t373 @t516)) % 0.41/0.81 (define @t518 () (= tptp.id @t70)) % 0.41/0.81 (define @t519 () (=> @t518 @t517)) % 0.41/0.81 (define @t520 () (=> @t484 @t519)) % 0.41/0.81 (define @t521 () (=> @t379 @t520)) % 0.41/0.81 (define @t522 () (=> @t295 @t521)) % 0.41/0.81 (define @t523 () (=> @t383 @t522)) % 0.41/0.81 (define @t524 () (=> @t487 @t523)) % 0.41/0.81 (define @t525 () (=> @t289 @t524)) % 0.41/0.81 (define @t526 () (=> @t392 @t525)) % 0.41/0.81 (define @t527 () (=> @t479 @t526)) % 0.41/0.81 (define @t528 () (=> @t396 @t527)) % 0.41/0.81 (define @t529 () (_ @t3 tptp.id)) % 0.41/0.81 (define @t530 () (_ tptp.ap @t529)) % 0.41/0.81 (define @t531 () (_ @t530 @t96)) % 0.41/0.81 (define @t532 () (_ tptp.ap @t22)) % 0.41/0.81 (define @t533 () (_ @t532 @t99)) % 0.41/0.81 (define @t534 () (= @t533 @t531)) % 0.41/0.81 (define @t535 () (not @t534)) % 0.41/0.81 (define @t536 () (or @t535 @t105)) % 0.41/0.81 (define @t537 () (@var "BOUND_VARIABLE_9440" tptp.term)) % 0.41/0.81 (define @t538 () (lambda (@list @t537) (_ @t530 @t537))) % 0.41/0.81 (define @t539 () (lambda (@list @t37 @t537) (_ (_ tptp.ap (_ @t3 @t37)) @t537))) % 0.41/0.81 (define @t540 () (lambda (@list @t5 @t37 @t2) @t275)) % 0.41/0.81 (define @t541 () (@list @t2)) % 0.41/0.81 (define @t542 () (_ @t276 tptp.id)) % 0.41/0.81 (define @t543 () (lambda @t154 (_ @t532 @t2))) % 0.41/0.81 (define @t544 () (lambda (@list @t37 @t2) @t275)) % 0.41/0.81 (define @t545 () (= (_ (_ (_ @t542 @t5) tptp.id) @t99) (_ (_ (_ @t542 @t2) tptp.id) @t96))) % 0.41/0.81 (define @t546 () (=> @t545 @t105)) % 0.41/0.81 (define @t547 () (forall @t102 @t546)) % 0.41/0.81 (define @t548 () (or @t535 @t95)) % 0.41/0.81 (define @t549 () (=> @t545 @t95)) % 0.41/0.81 (define @t550 () (forall @t102 @t549)) % 0.41/0.81 (define @t551 () (= @t5 @t22)) % 0.41/0.81 (define @t552 () (= @t1 @t67)) % 0.41/0.81 (define @t553 () (= @t1 @t45)) % 0.41/0.81 (define @t554 () (@list @t296)) % 0.41/0.81 (define @t555 () (forall @t554 @t499)) % 0.41/0.81 (define @t556 () (forall @t554 @t297)) % 0.41/0.81 (define @t557 () (@list @t5)) % 0.41/0.81 (define @t558 () (or @t312 @t308 @t498 @t556)) % 0.41/0.81 (define @t559 () (forall @t23 @t305)) % 0.41/0.81 (define @t560 () (or @t312 @t308 @t498 @t559)) % 0.41/0.81 (define @t561 () (or @t308 @t498 @t559)) % 0.41/0.81 (define @t562 () (=> @t497 @t559)) % 0.41/0.81 (define @t563 () (=> @t307 @t562)) % 0.41/0.81 (define @t564 () (or @t495 @t132)) % 0.41/0.81 (define @t565 () (not @t136)) % 0.41/0.81 (define @t566 () (or @t565 @t170)) % 0.41/0.81 (define @t567 () (not @t84)) % 0.41/0.81 (define @t568 () (or @t567 @t565 @t135)) % 0.41/0.81 (define @t569 () (not @t80)) % 0.41/0.81 (define @t570 () (or @t569 @t84)) % 0.41/0.81 (define @t571 () (or @t319 @t316)) % 0.41/0.81 (define @t572 () (or @t308 @t498 @t571)) % 0.41/0.81 (define @t573 () (forall @t320 @t572)) % 0.41/0.81 (define @t574 () (@list @t315 @t314)) % 0.41/0.81 (define @t575 () (forall @t574 @t572)) % 0.41/0.81 (define @t576 () (forall @t574 @t571)) % 0.41/0.81 (define @t577 () (or @t308 @t498 @t576)) % 0.41/0.81 (define @t578 () (_ @t83 @t287)) % 0.41/0.81 (define @t579 () (forall @t19 (or @t328 @t578))) % 0.41/0.81 (define @t580 () (or @t308 @t498 @t579)) % 0.41/0.81 (define @t581 () (=> @t497 @t579)) % 0.41/0.81 (define @t582 () (or @t328 @t165)) % 0.41/0.81 (define @t583 () (not @t153)) % 0.41/0.81 (define @t584 () (or @t583 @t152)) % 0.41/0.81 (define @t585 () (or @t324 @t323)) % 0.41/0.81 (define @t586 () (or @t328 @t306 @t585)) % 0.41/0.81 (define @t587 () (forall @t330 @t586)) % 0.41/0.81 (define @t588 () (@list @t322)) % 0.41/0.81 (define @t589 () (forall @t588 @t586)) % 0.41/0.81 (define @t590 () (forall @t588 @t585)) % 0.41/0.81 (define @t591 () (or @t328 @t306 @t590)) % 0.41/0.81 (define @t592 () (tptp.sub @t2 @t321)) % 0.41/0.81 (define @t593 () (_ @t83 @t592)) % 0.41/0.81 (define @t594 () (forall @t154 (or @t318 @t593))) % 0.41/0.81 (define @t595 () (or @t328 @t567 @t594)) % 0.41/0.81 (define @t596 () (=> @t84 @t594)) % 0.41/0.81 (define @t597 () (or @t583 @t157)) % 0.41/0.81 (define @t598 () (@list @t332)) % 0.41/0.81 (define @t599 () (forall @t598 @t336)) % 0.41/0.81 (define @t600 () (forall @t598 @t333)) % 0.41/0.81 (define @t601 () (or @t312 @t308 @t335 @t600)) % 0.41/0.81 (define @t602 () (or @t312 @t308 @t335 @t559)) % 0.41/0.81 (define @t603 () (or @t308 @t335 @t559)) % 0.41/0.81 (define @t604 () (=> @t334 @t559)) % 0.41/0.81 (define @t605 () (=> @t307 @t604)) % 0.41/0.81 (define @t606 () (or @t567 @t132)) % 0.41/0.81 (define @t607 () (not @t114)) % 0.41/0.81 (define @t608 () (or @t607 @t95)) % 0.41/0.81 (define @t609 () (not @t109)) % 0.41/0.81 (define @t610 () (or @t609 @t95)) % 0.41/0.81 (define @t611 () (not @t101)) % 0.41/0.81 (define @t612 () (or @t611 @t105)) % 0.41/0.81 (define @t613 () (or @t611 @t95)) % 0.41/0.81 (define @t614 () (or @t356 @t355)) % 0.41/0.81 (define @t615 () (or @t361 @t359 @t614)) % 0.41/0.81 (define @t616 () (forall @t363 @t615)) % 0.41/0.81 (define @t617 () (@list @t354)) % 0.41/0.81 (define @t618 () (forall @t617 @t615)) % 0.41/0.81 (define @t619 () (forall @t617 @t614)) % 0.41/0.81 (define @t620 () (or @t361 @t359 @t619)) % 0.41/0.81 (define @t621 () (not @t90)) % 0.41/0.81 (define @t622 () (or @t621 @t359 @t311)) % 0.41/0.81 (define @t623 () (=> @t358 @t311)) % 0.41/0.81 (define @t624 () (or @t569 @t567 @t86)) % 0.41/0.81 (define @t625 () (or @t569 @t79)) % 0.41/0.81 (define @t626 () (= @t1 @t74)) % 0.41/0.81 (define @t627 () (= @t1 @t50)) % 0.41/0.81 (define @t628 () (= @t5 @t18)) % 0.41/0.81 (define @t629 () (@quantifiers_skolemize @t283 3)) % 0.41/0.81 (define @t630 () (@quantifiers_skolemize @t283 2)) % 0.41/0.81 (define @t631 () (tptp.sub (@quantifiers_skolemize @t283 0) @t280)) % 0.41/0.81 (define @t632 () (tptp.sub (@quantifiers_skolemize @t283 1) @t280)) % 0.41/0.81 (define @t633 () (not (= (tptp.ap @t632 @t629) (tptp.ap @t631 @t630)))) % 0.41/0.81 (define @t634 () (or @t633 (= @t629 @t630))) % 0.41/0.81 (assume @p1 @t15) % 0.41/0.81 (assume @p2 @t21) % 0.41/0.81 (assume @p3 @t25) % 0.41/0.81 (assume @p4 @t36) % 0.41/0.81 (assume @p5 @t44) % 0.41/0.81 (assume @p6 @t48) % 0.41/0.81 (assume @p7 @t52) % 0.41/0.81 (assume @p8 @t60) % 0.41/0.81 (assume @p9 @t66) % 0.41/0.81 (assume @p10 @t69) % 0.41/0.81 (assume @p11 @t71) % 0.41/0.81 (assume @p12 @t76) % 0.41/0.81 (assume @p13 (= tptp.ulamvar1 @t77)) % 0.41/0.81 (assume @p14 @t82) % 0.41/0.81 (assume @p15 @t94) % 0.41/0.81 (assume @p16 @t104) % 0.41/0.81 (assume @p17 @t107) % 0.41/0.81 (assume @p18 @t112) % 0.41/0.81 (assume @p19 @t116) % 0.41/0.81 (assume @p20 @t122) % 0.41/0.81 (assume @p21 @t126) % 0.41/0.81 (assume @p22 @t130) % 0.41/0.81 (assume @p23 @t142) % 0.41/0.81 (assume @p24 (= tptp.pushprop_lem0 (forall @t146 (exists @t145 @t144)))) % 0.41/0.81 (assume @p25 (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0))))))))))))))))))))))))) % 0.41/0.81 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 0.41/0.81 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t83 @t148 @t5 @t1 @t2) (=> @t84 (_ @t148 (_ @t6 (_ @t147 @t1))))))) % 0.41/0.81 (assume @p28 (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1))))))))))))))))))))))))) % 0.41/0.81 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 0.41/0.81 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t149 (=> @t84 (=> @t144 (_ @t143 tptp.one)))))) % 0.41/0.81 (assume @p31 (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2))))))))))))))))))))))))) % 0.41/0.81 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 0.41/0.81 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t149 (=> @t144 (=> @t155 (forall @t151 (=> (_ tptp.var @t99) (=> (_ @t143 @t99) (_ @t143 (_ @t150 tptp.sh)))))))))) % 0.41/0.81 (assume @p34 (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2))))))))))))))))))))))))) % 0.41/0.81 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 0.41/0.81 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t149 (=> @t144 (=> (forall @t154 (=> @t153 @t159)) @t158))))) % 0.41/0.81 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 0.41/0.81 (assume @p38 @t163) % 0.41/0.81 (assume @p39 (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop))))))))))))))))))))))))) % 0.41/0.81 (assume @p40 (= tptp.pushprop_lthm_orig @t164)) % 0.41/0.81 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t164))) % 0.41/0.81 (assume @p42 @t177) % 0.41/0.81 (assume @p43 (= tptp.induction2lem_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar @t178)))))))))))))))))))))))) % 0.41/0.81 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t178)))))))))) % 0.41/0.81 (assume @p45 @t183) % 0.41/0.81 (assume @p46 (= tptp.induction2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop @t184)))))))))))))))))))))))))) % 0.41/0.81 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t184))) % 0.41/0.81 (assume @p48 @t186) % 0.41/0.81 (assume @p49 (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid)))))))))))))))))))))))))))) % 0.41/0.81 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 0.41/0.81 (assume @p51 @t188) % 0.41/0.81 (assume @p52 (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 0.41/0.81 (assume @p54 @t194) % 0.41/0.81 (assume @p55 (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1)))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 0.41/0.81 (assume @p57 @t197) % 0.41/0.81 (assume @p58 @t227) % 0.41/0.81 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 0.41/0.81 (assume @p60 (= tptp.hoaslaminj (forall @t240 (=> @t239 (forall (@list @t228) (=> (forall @t236 (= (_ (_ tptp.sub @t229) @t37) (_ (_ @t228 @t38) @t61))) (=> (= @t235 (_ @t234 (lambda @t233 @t229))) (forall @t233 (= @t232 @t229))))))))) % 0.41/0.81 (assume @p61 (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj)))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 0.41/0.81 (assume @p63 (= tptp.hoaslamnotap (forall @t240 (=> @t239 (forall @t110 (not (= (_ @t234 (lambda (@list @t1 @t99) (_ @t231 @t99))) @t241))))))) % 0.41/0.81 (assume @p64 (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 0.41/0.81 (assume @p66 (= tptp.hoaslamnotvar (forall @t240 (=> @t239 (not (_ (_ @t242 @t235) tptp.id)))))) % 0.41/0.81 (assume @p67 (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar)))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 0.41/0.81 (assume @p69 (= tptp.hoasapnotvar (forall @t110 (not (_ (_ @t242 @t241) tptp.id))))) % 0.41/0.81 (assume @p70 (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 0.41/0.81 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t245 (exists @t145 @t244)))) % 0.41/0.81 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 0.41/0.81 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t255 (=> @t254 (=> @t253 (=> @t249 (=> @t244 (forall @t23 (=> @t80 @t246))))))))) % 0.41/0.81 (assume @p75 (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t255 (=> @t254 (=> @t253 (=> @t257 (=> @t244 (forall @t110 (=> @t246 (=> @t159 (_ @t143 @t10))))))))))) % 0.41/0.81 (assume @p77 (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t154 (exists @t240 (forall @t19 (= @t232 @t156)))))) % 0.41/0.81 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 0.41/0.81 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t255 (=> @t254 (=> @t253 @t260))))) % 0.41/0.81 (assume @p81 (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2)))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 0.41/0.81 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t255 @t260))) % 0.41/0.81 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 0.41/0.81 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t245 (=> @t254 (=> @t253 (=> @t249 (forall @t23 (=> @t80 @t248)))))))) % 0.41/0.81 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t261)) % 0.41/0.81 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t261)) % 0.41/0.81 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t245 (=> @t254 (=> @t253 (=> @t257 (forall @t110 (=> @t248 (=> @t256 (_ (_ @t247 @t10) tptp.id)))))))))) % 0.41/0.81 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t262)) % 0.41/0.81 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t262)) % 0.41/0.81 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t245 (=> @t259 @t264)))) % 0.41/0.81 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 0.41/0.81 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t245 (=> (forall @t240 (=> (exists @t151 (forall @t236 (and (= @t238 (_ (_ tptp.sub (_ @t150 @t16)) @t37)) (= (_ @t150 @t62) @t237)))) @t258)) @t264)))) % 0.41/0.81 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t245 (=> @t254 (=> @t253 @t265))))) % 0.41/0.81 (assume @p95 (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3)))))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 0.41/0.81 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t245 @t265))) % 0.41/0.81 (assume @p98 (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a)))))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 0.41/0.81 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t154 (exists @t240 (= (_ @t3 @t70) @t266))))) % 0.41/0.81 (assume @p101 (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b)))))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 0.41/0.81 (assume @p103 (= tptp.hoasinduction (forall @t245 (=> @t254 (=> @t253 (=> @t249 @t267)))))) % 0.41/0.81 (assume @p104 (= tptp.hoasinduction_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar @t268)))))))))))))))))))))))))))))))))))) % 0.41/0.81 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t268))) % 0.41/0.81 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 0.41/0.81 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t245 @t267))) % 0.41/0.81 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 0.41/0.81 (assume @p109 @t269) % 0.41/0.81 (assume @p110 true) % 0.41/0.81 (step @p111 (= tptp.pushprop_p_and_p_prime @t273) :rule refl :args (@t273)) % 0.41/0.81 (step @p112 (= tptp.hoasap @t276) :rule refl :args (@t276)) % 0.41/0.81 (step @p113 (= tptp.hoaslam @t277) :rule refl :args (@t277)) % 0.41/0.81 (step @p114 (= tptp.hoasvar @t278) :rule refl :args (@t278)) % 0.41/0.81 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t279) :rule refl :args (@t279)) % 0.41/0.81 (step @p116 :rule refl :args (@t367)) % 0.41/0.81 (step @p117 :rule refl :args (@t368)) % 0.41/0.81 (step @p118 :rule refl :args (@t77)) % 0.41/0.81 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t77 @t368))) % 0.41/0.81 (step @p120 :rule symm :premises (@p119)) % 0.41/0.81 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 0.41/0.81 (step @p122 :rule cong :premises (@p121 @p116) :args (@t369)) % 0.41/0.81 (step @p123 :rule refl :args (@t373)) % 0.41/0.81 (step @p124 :rule cong :premises (@p123 @p122) :args (@t374)) % 0.41/0.81 (step @p125 :rule refl :args (@t290)) % 0.41/0.81 (step @p126 :rule cong :premises (@p125 @p124) :args (@t375)) % 0.41/0.81 (step @p127 :rule refl :args (@t379)) % 0.41/0.81 (step @p128 :rule cong :premises (@p127 @p126) :args (@t380)) % 0.41/0.81 (step @p129 :rule refl :args (@t295)) % 0.41/0.81 (step @p130 :rule cong :premises (@p129 @p128) :args (@t381)) % 0.41/0.81 (step @p131 :rule refl :args (@t383)) % 0.41/0.81 (step @p132 :rule cong :premises (@p131 @p130) :args (@t384)) % 0.41/0.81 (step @p133 :rule refl :args (@t291)) % 0.41/0.81 (step @p134 :rule cong :premises (@p133 @p132) :args (@t385)) % 0.41/0.81 (step @p135 :rule refl :args (@t289)) % 0.41/0.81 (step @p136 :rule cong :premises (@p135 @p134) :args (@t386)) % 0.41/0.81 (step @p137 :rule refl :args (@t392)) % 0.41/0.81 (step @p138 :rule cong :premises (@p137 @p136) :args (@t393)) % 0.41/0.81 (step @p139 :rule refl :args (@t284)) % 0.41/0.81 (step @p140 :rule cong :premises (@p139 @p138) :args (@t394)) % 0.41/0.81 (step @p141 :rule refl :args (@t396)) % 0.41/0.81 (step @p142 :rule cong :premises (@p141 @p140) :args (@t397)) % 0.41/0.81 (step @p143 :rule refl :args (@t400)) % 0.41/0.81 (step @p144 :rule cong :premises (@p143 @p142) :args (@t401)) % 0.41/0.81 (step @p145 :rule cong :premises (@p144) :args ((not @t401))) % 0.41/0.81 (step @p146 :rule bool-impl-true2 :args (@t374)) % 0.41/0.81 (step @p147 :rule refl :args (@t105)) % 0.41/0.81 (step @p148 :rule refl :args (@t99)) % 0.41/0.81 (step @p149 :rule refl :args (@t280)) % 0.41/0.81 (step @p150 :rule refl :args (@t70)) % 0.41/0.81 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t70 @t280))) % 0.41/0.81 (step @p152 :rule symm :premises (@p151)) % 0.41/0.81 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.41/0.81 (step @p154 :rule refl :args (@t5)) % 0.41/0.81 (step @p155 :rule cong :premises (@p154 @p153) :args (@t402)) % 0.41/0.81 (step @p156 :rule cong :premises (@p155 @p148) :args (@t403)) % 0.41/0.81 (step @p157 :rule refl :args (@t96)) % 0.41/0.81 (step @p158 :rule refl :args (@t2)) % 0.41/0.81 (step @p159 :rule cong :premises (@p158 @p153) :args (@t404)) % 0.41/0.81 (step @p160 :rule cong :premises (@p159 @p157) :args (@t405)) % 0.41/0.81 (step @p161 :rule cong :premises (@p160 @p156) :args (@t406)) % 0.41/0.81 (step @p162 :rule cong :premises (@p161) :args (@t407)) % 0.41/0.81 (step @p163 :rule nary_cong :premises (@p162 @p147) :args (@t408)) % 0.41/0.81 (step @p164 :rule cong :premises (@p163) :args ((forall @t102 @t408))) % 0.41/0.81 (step @p165 :rule refl :args (@t105)) % 0.41/0.81 (step @p166 :rule eq-symm :args (@t403 @t405)) % 0.41/0.81 (step @p167 :rule cong :premises (@p166) :args (@t409)) % 0.41/0.81 (step @p168 :rule nary_cong :premises (@p167 @p165) :args (@t410)) % 0.41/0.81 (step @p169 :rule cong :premises (@p168) :args (@t411)) % 0.41/0.81 (step @p170 :rule trans :premises (@p169 @p164)) % 0.41/0.81 (step @p171 :rule refl :args (@t95)) % 0.41/0.81 (step @p172 :rule nary_cong :premises (@p162 @p171) :args (@t412)) % 0.41/0.81 (step @p173 :rule cong :premises (@p172) :args ((forall @t102 @t412))) % 0.41/0.81 (step @p174 :rule refl :args (@t95)) % 0.41/0.81 (step @p175 :rule nary_cong :premises (@p167 @p174) :args (@t413)) % 0.41/0.81 (step @p176 :rule cong :premises (@p175) :args (@t414)) % 0.41/0.81 (step @p177 :rule trans :premises (@p176 @p173)) % 0.41/0.81 (step @p178 :rule cong :premises (@p177 @p170) :args (@t415)) % 0.41/0.81 (step @p179 :rule cong :premises (@p154 @p155) :args (@t416)) % 0.41/0.81 (step @p180 :rule cong :premises (@p179) :args (@t417)) % 0.41/0.81 (step @p181 :rule nary_cong :premises (@p135 @p180) :args (@t418)) % 0.41/0.81 (step @p182 :rule cong :premises (@p181 @p178) :args (@t419)) % 0.41/0.81 (step @p183 :rule refl :args (@t1)) % 0.41/0.81 (step @p184 :rule cong :premises (@p183 @p153) :args (@t420)) % 0.41/0.81 (step @p185 :rule cong :premises (@p183 @p184) :args (@t421)) % 0.41/0.81 (step @p186 :rule cong :premises (@p185) :args (@t422)) % 0.41/0.81 (step @p187 :rule cong :premises (@p153 @p183) :args (@t423)) % 0.41/0.81 (step @p188 :rule cong :premises (@p183 @p187) :args (@t424)) % 0.41/0.81 (step @p189 :rule cong :premises (@p188) :args (@t425)) % 0.41/0.81 (step @p190 :rule nary_cong :premises (@p129 @p189 @p186) :args (@t426)) % 0.41/0.81 (step @p191 :rule cong :premises (@p190 @p182) :args (@t427)) % 0.41/0.81 (step @p192 :rule refl :args (@t297)) % 0.41/0.81 (step @p193 :rule refl :args (@t299)) % 0.41/0.81 (step @p194 :rule cong :premises (@p158 @p153) :args (@t428)) % 0.41/0.81 (step @p195 :rule cong :premises (@p154 @p194) :args (@t429)) % 0.41/0.81 (step @p196 :rule cong :premises (@p195) :args (@t430)) % 0.41/0.81 (step @p197 :rule refl :args (@t301)) % 0.41/0.81 (step @p198 :rule nary_cong :premises (@p197 @p196) :args (@t431)) % 0.41/0.81 (step @p199 :rule cong :premises (@p198) :args (@t432)) % 0.41/0.81 (step @p200 :rule cong :premises (@p199) :args (@t433)) % 0.41/0.81 (step @p201 :rule nary_cong :premises (@p200 @p193) :args (@t434)) % 0.41/0.81 (step @p202 :rule cong :premises (@p201) :args (@t435)) % 0.41/0.81 (step @p203 :rule cong :premises (@p202) :args (@t436)) % 0.41/0.81 (step @p204 :rule refl :args (@t308)) % 0.41/0.81 (step @p205 :rule refl :args (@t312)) % 0.41/0.81 (step @p206 :rule nary_cong :premises (@p205 @p204 @p203 @p192) :args (@t437)) % 0.41/0.81 (step @p207 :rule cong :premises (@p206) :args (@t438)) % 0.41/0.81 (step @p208 :rule cong :premises (@p207 @p191) :args (@t439)) % 0.41/0.81 (step @p209 :rule refl :args (@t316)) % 0.41/0.81 (step @p210 :rule refl :args (@t319)) % 0.41/0.81 (step @p211 :rule nary_cong :premises (@p204 @p203 @p210 @p209) :args (@t440)) % 0.41/0.81 (step @p212 :rule cong :premises (@p211) :args (@t441)) % 0.41/0.81 (step @p213 :rule cong :premises (@p212 @p208) :args (@t442)) % 0.41/0.81 (step @p214 :rule refl :args (@t331)) % 0.41/0.81 (step @p215 :rule cong :premises (@p214 @p213) :args (@t443)) % 0.41/0.81 (step @p216 :rule refl :args (@t337)) % 0.41/0.81 (step @p217 :rule cong :premises (@p216 @p215) :args (@t444)) % 0.41/0.81 (step @p218 :rule refl :args (@t339)) % 0.41/0.81 (step @p219 :rule cong :premises (@p218 @p217) :args (@t445)) % 0.41/0.81 (step @p220 :rule refl :args (@t341)) % 0.41/0.81 (step @p221 :rule cong :premises (@p220 @p219) :args (@t446)) % 0.41/0.81 (step @p222 :rule refl :args (@t343)) % 0.41/0.81 (step @p223 :rule cong :premises (@p222 @p221) :args (@t447)) % 0.41/0.81 (step @p224 :rule refl :args (@t346)) % 0.41/0.81 (step @p225 :rule cong :premises (@p224 @p223) :args (@t448)) % 0.41/0.81 (step @p226 :rule refl :args (@t348)) % 0.41/0.81 (step @p227 :rule cong :premises (@p226 @p225) :args (@t449)) % 0.41/0.81 (step @p228 :rule refl :args (@t352)) % 0.41/0.81 (step @p229 :rule cong :premises (@p228 @p227) :args (@t450)) % 0.41/0.81 (step @p230 :rule refl :args (@t353)) % 0.41/0.81 (step @p231 :rule cong :premises (@p230 @p229) :args (@t451)) % 0.41/0.81 (step @p232 :rule refl :args (@t364)) % 0.41/0.81 (step @p233 :rule cong :premises (@p232 @p231) :args (@t452)) % 0.41/0.81 (step @p234 :rule refl :args (@t366)) % 0.41/0.81 (step @p235 :rule cong :premises (@p234 @p233) :args (@t453)) % 0.41/0.81 (step @p236 :rule refl :args (@t77)) % 0.41/0.81 (step @p237 :rule cong :premises (@p236 @p235) :args (@t454)) % 0.41/0.81 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((tptp.sub @t5 @t29))) % 0.41/0.81 (step @p1158 :rule refl :args ((tptp.push tptp.one @t27))) % 0.41/0.81 (step @p1159 :rule refl :args (@t387)) % 0.41/0.81 (step @p1160 :rule refl :args (tptp.one)) % 0.41/0.81 (step @p1161 :rule cong :premises (@p1160 @p1159) :args (@t388)) % 0.41/0.81 (step @p1162 :rule trans :premises (@p1161 @p1158)) % 0.41/0.81 (step @p1163 :rule cong :premises (@p154 @p1162) :args (@t389)) % 0.41/0.81 (step @p1164 :rule trans :premises (@p1163 @p1157)) % 0.41/0.81 (step @p1165 :rule cong :premises (@p1164) :args (@t390)) % 0.41/0.81 (step @p1166 :rule trans :premises (@p1165 @p1156)) % 0.41/0.81 (step @p1167 :rule refl :args (tptp.lam)) % 0.41/0.81 (step @p1168 :rule ho_cong :premises (@p1167 @p1164)) % 0.41/0.81 (step @p1169 :rule cong :premises (@p1168 @p1166) :args ((= (_ tptp.lam @t389) @t390))) % 0.41/0.81 (step @p1170 :rule symm :premises (@p1169)) % 0.41/0.81 (step @p1171 :rule refl :args (@t31)) % 0.41/0.81 (step @p1172 :rule eq_resolve :premises (@p1171 @p1170)) % 0.41/0.81 (step @p1173 :rule ho_cong :premises (@p450 @p1162)) % 0.41/0.81 (step @p1174 :rule cong :premises (@p1173 @p1164) :args ((= (_ @t6 @t388) @t389))) % 0.41/0.81 (step @p1175 :rule symm :premises (@p1174)) % 0.41/0.81 (step @p1176 :rule refl :args (@t30)) % 0.41/0.81 (step @p1177 :rule eq_resolve :premises (@p1176 @p1175)) % 0.41/0.81 (step @p1178 :rule refl :args (@t28)) % 0.41/0.81 (step @p1179 :rule ho_cong :premises (@p1178 @p1159)) % 0.41/0.81 (step @p1180 :rule cong :premises (@p1179 @p1162) :args ((= (_ @t28 @t387) @t388))) % 0.41/0.81 (step @p1181 :rule symm :premises (@p1180)) % 0.41/0.81 (step @p1182 :rule refl :args (@t29)) % 0.41/0.81 (step @p1183 :rule eq_resolve :premises (@p1182 @p1181)) % 0.41/0.81 (step @p1184 :rule refl :args (@t27)) % 0.41/0.81 (step @p1185 :rule cong :premises (@p1184 @p1159) :args ((= @t27 @t387))) % 0.41/0.81 (step @p1186 :rule symm :premises (@p1185)) % 0.41/0.81 (step @p1187 :rule eq_resolve :premises (@p1184 @p1186)) % 0.41/0.81 (step @p1188 :rule ho_cong :premises (@p1178 @p1187)) % 0.41/0.81 (step @p1189 :rule trans :premises (@p1188 @p1183)) % 0.41/0.81 (step @p1190 :rule ho_cong :premises (@p450 @p1189)) % 0.41/0.81 (step @p1191 :rule trans :premises (@p1190 @p1177)) % 0.41/0.81 (step @p1192 :rule ho_cong :premises (@p1167 @p1191)) % 0.41/0.81 (step @p1193 :rule trans :premises (@p1192 @p1172)) % 0.41/0.81 (step @p1194 :rule refl :args ((tptp.sub @t32 @t1))) % 0.41/0.81 (step @p1195 :rule cong :premises (@p576 @p183) :args (@t391)) % 0.41/0.81 (step @p1196 :rule trans :premises (@p1195 @p1194)) % 0.41/0.81 (step @p1197 :rule ho_cong :premises (@p467 @p576)) % 0.41/0.81 (step @p1198 :rule ho_cong :premises (@p1197 @p183)) % 0.41/0.81 (step @p1199 :rule cong :premises (@p1198 @p1196) :args ((= (_ (_ tptp.sub @t298) @t1) @t391))) % 0.41/0.81 (step @p1200 :rule symm :premises (@p1199)) % 0.41/0.81 (step @p1201 :rule refl :args (@t33)) % 0.41/0.81 (step @p1202 :rule eq_resolve :premises (@p1201 @p1200)) % 0.41/0.81 (step @p1203 :rule ho_cong :premises (@p467 @p588)) % 0.41/0.81 (step @p1204 :rule ho_cong :premises (@p1203 @p183)) % 0.41/0.81 (step @p1205 :rule trans :premises (@p1204 @p1202)) % 0.41/0.81 (step @p1206 :rule cong :premises (@p1205 @p1193) :args (@t34)) % 0.41/0.81 (step @p1207 :rule cong :premises (@p1206) :args (@t35)) % 0.41/0.81 (step @p1208 :rule refl :args (tptp.axabs)) % 0.41/0.81 (step @p1209 :rule cong :premises (@p1208 @p1207) :args (@t36)) % 0.41/0.81 (step @p1210 :rule eq_resolve :premises (@p4 @p1209)) % 0.41/0.81 (step @p1211 :rule cong :premises (@p1210 @p1155) :args (@t223)) % 0.41/0.81 (step @p1212 :rule refl :args (tptp.axvarid)) % 0.41/0.81 (step @p1213 :rule cong :premises (@p1212 @p445) :args (@t25)) % 0.41/0.81 (step @p1214 :rule eq_resolve :premises (@p3 @p1213)) % 0.41/0.81 (step @p1215 :rule cong :premises (@p1214 @p1211) :args (@t224)) % 0.41/0.81 (step @p1216 :rule refl :args ((tptp.sub tptp.one @t16))) % 0.41/0.81 (step @p1217 :rule cong :premises (@p1160 @p783) :args (@t395)) % 0.41/0.81 (step @p1218 :rule trans :premises (@p1217 @p1216)) % 0.41/0.81 (step @p1219 :rule refl :args (@t17)) % 0.41/0.81 (step @p1220 :rule ho_cong :premises (@p1219 @p783)) % 0.41/0.81 (step @p1221 :rule cong :premises (@p1220 @p1218) :args ((= (_ @t17 @t321) @t395))) % 0.41/0.81 (step @p1222 :rule symm :premises (@p1221)) % 0.41/0.81 (step @p1223 :rule refl :args (@t18)) % 0.41/0.81 (step @p1224 :rule eq_resolve :premises (@p1223 @p1222)) % 0.41/0.81 (step @p1225 :rule ho_cong :premises (@p1219 @p802)) % 0.41/0.81 (step @p1226 :rule trans :premises (@p1225 @p1224)) % 0.41/0.81 (step @p1227 :rule cong :premises (@p154 @p1226) :args (@t628)) % 0.41/0.81 (step @p1228 :rule cong :premises (@p1227) :args ((forall @t19 @t628))) % 0.41/0.81 (step @p1229 :rule eq-symm :args (@t18 @t5)) % 0.41/0.81 (step @p1230 :rule cong :premises (@p1229) :args (@t20)) % 0.41/0.81 (step @p1231 :rule trans :premises (@p1230 @p1228)) % 0.41/0.81 (step @p1232 :rule refl :args (tptp.axvarcons)) % 0.41/0.81 (step @p1233 :rule cong :premises (@p1232 @p1231) :args (@t21)) % 0.41/0.81 (step @p1234 :rule eq_resolve :premises (@p2 @p1233)) % 0.41/0.81 (step @p1235 :rule cong :premises (@p1234 @p1215) :args (@t225)) % 0.41/0.81 (step @p1236 :rule refl :args ((tptp.ap @t7 @t4))) % 0.41/0.81 (step @p1237 :rule cong :premises (@p464 @p721) :args (@t398)) % 0.41/0.81 (step @p1238 :rule trans :premises (@p1237 @p1236)) % 0.41/0.81 (step @p1239 :rule ho_cong :premises (@p345 @p464)) % 0.41/0.81 (step @p1240 :rule ho_cong :premises (@p1239 @p721)) % 0.41/0.81 (step @p1241 :rule cong :premises (@p1240 @p1238) :args ((= (_ (_ tptp.ap @t287) @t325) @t398))) % 0.41/0.81 (step @p1242 :rule symm :premises (@p1241)) % 0.41/0.81 (step @p1243 :rule refl :args (@t8)) % 0.41/0.81 (step @p1244 :rule eq_resolve :premises (@p1243 @p1242)) % 0.41/0.81 (step @p1245 :rule ho_cong :premises (@p345 @p477)) % 0.41/0.81 (step @p1246 :rule ho_cong :premises (@p1245 @p732)) % 0.41/0.81 (step @p1247 :rule trans :premises (@p1246 @p1244)) % 0.41/0.81 (step @p1248 :rule refl :args ((tptp.sub @t10 @t1))) % 0.41/0.81 (step @p1249 :rule cong :premises (@p639 @p183) :args (@t399)) % 0.41/0.81 (step @p1250 :rule trans :premises (@p1249 @p1248)) % 0.41/0.81 (step @p1251 :rule ho_cong :premises (@p467 @p639)) % 0.41/0.81 (step @p1252 :rule ho_cong :premises (@p1251 @p183)) % 0.41/0.81 (step @p1253 :rule cong :premises (@p1252 @p1250) :args ((= (_ (_ tptp.sub @t303) @t1) @t399))) % 0.41/0.81 (step @p1254 :rule symm :premises (@p1253)) % 0.41/0.81 (step @p1255 :rule refl :args (@t11)) % 0.41/0.81 (step @p1256 :rule eq_resolve :premises (@p1255 @p1254)) % 0.41/0.81 (step @p1257 :rule ho_cong :premises (@p467 @p650)) % 0.41/0.81 (step @p1258 :rule ho_cong :premises (@p1257 @p183)) % 0.41/0.81 (step @p1259 :rule trans :premises (@p1258 @p1256)) % 0.41/0.81 (step @p1260 :rule cong :premises (@p1259 @p1247) :args (@t12)) % 0.41/0.81 (step @p1261 :rule cong :premises (@p1260) :args (@t14)) % 0.41/0.81 (step @p1262 :rule refl :args (tptp.axapp)) % 0.41/0.81 (step @p1263 :rule cong :premises (@p1262 @p1261) :args (@t15)) % 0.41/0.81 (step @p1264 :rule eq_resolve :premises (@p1 @p1263)) % 0.41/0.81 (step @p1265 :rule cong :premises (@p1264 @p1235) :args (@t226)) % 0.41/0.81 (step @p1266 :rule refl :args (tptp.hoasapinj2_gthm)) % 0.41/0.81 (step @p1267 :rule cong :premises (@p1266 @p1265) :args (@t227)) % 0.41/0.81 (step @p1268 :rule eq_resolve :premises (@p58 @p1267)) % 0.41/0.81 (step @p1269 :rule trans :premises (@p1268 @p340)) % 0.41/0.81 (step @p1270 :rule cong :premises (@p1269) :args (@t269)) % 0.41/0.81 (step @p1271 :rule trans :premises (@p1270 @p252)) % 0.41/0.81 (step @p1272 :rule trans :premises (@p1271 @p145)) % 0.41/0.81 (step @p1273 :rule eq_resolve :premises (@p109 @p1272)) % 0.41/0.81 (step @p1274 :rule not_implies_elim2 :premises (@p1273)) % 0.41/0.81 (step @p1275 :rule not_implies_elim2 :premises (@p1274)) % 0.41/0.81 (step @p1276 :rule not_implies_elim2 :premises (@p1275)) % 0.41/0.81 (step @p1277 :rule not_implies_elim2 :premises (@p1276)) % 0.41/0.81 (step @p1278 :rule not_implies_elim2 :premises (@p1277)) % 0.41/0.81 (step @p1279 :rule not_implies_elim2 :premises (@p1278)) % 0.41/0.81 (step @p1280 :rule not_implies_elim2 :premises (@p1279)) % 0.41/0.81 (step @p1281 :rule not_implies_elim2 :premises (@p1280)) % 0.41/0.81 (step @p1282 :rule not_implies_elim2 :premises (@p1281)) % 0.41/0.81 (step @p1283 :rule not_implies_elim2 :premises (@p1282)) % 0.41/0.81 (step @p1284 :rule not_implies_elim2 :premises (@p1283)) % 0.41/0.81 (step @p1285 :rule not_implies_elim2 :premises (@p1284)) % 0.41/0.81 (step @p1286 :rule not_implies_elim2 :premises (@p1285)) % 0.41/0.81 (step @p1287 :rule not_implies_elim2 :premises (@p1286)) % 0.41/0.81 (step @p1288 :rule not_implies_elim2 :premises (@p1287)) % 0.41/0.81 (step @p1289 :rule not_implies_elim1 :premises (@p1288)) % 0.41/0.81 (step @p1290 :rule not_implies_elim2 :premises (@p1288)) % 0.41/0.81 (step @p1291 :rule not_implies_elim2 :premises (@p1290)) % 0.41/0.81 (step @p1292 :rule not_implies_elim2 :premises (@p1291)) % 0.41/0.81 (step @p1293 :rule not_implies_elim2 :premises (@p1292)) % 0.41/0.81 (step @p1294 :rule not_implies_elim2 :premises (@p1293)) % 0.41/0.81 (step @p1295 :rule not_implies_elim2 :premises (@p1294)) % 0.41/0.81 (step @p1296 :rule not_implies_elim2 :premises (@p1295)) % 0.41/0.81 (step @p1297 :rule not_implies_elim2 :premises (@p1296)) % 0.41/0.81 (step @p1298 :rule not_implies_elim2 :premises (@p1297)) % 0.41/0.81 (step @p1299 :rule not_implies_elim2 :premises (@p1298)) % 0.41/0.81 (step @p1300 :rule not_implies_elim2 :premises (@p1299)) % 0.41/0.81 (step @p1301 :rule not_implies_elim2 :premises (@p1300)) % 0.41/0.81 (step @p1302 :rule not_implies_elim2 :premises (@p1301)) % 0.41/0.81 (step @p1303 :rule skolemize :premises (@p1302)) % 0.41/0.81 (step @p1304 :rule eq-symm :args (@t629 @t630)) % 0.41/0.81 (step @p1305 :rule refl :args (@t633)) % 0.41/0.81 (step @p1306 :rule nary_cong :premises (@p1305 @p1304) :args (@t634)) % 0.41/0.81 (step @p1307 :rule cong :premises (@p228 @p1306) :args ((=> @t352 @t634))) % 0.41/0.81 (assume-push @p1315 @t352) % 0.41/0.81 (step @p1309 :rule instantiate :premises (@p1289) :args ((@list @t632 @t631 @t629 @t630))) % 0.41/0.81 (step-pop @p1316 :rule scope :premises (@p1309)) % 0.41/0.81 (step @p1310 :rule process_scope :premises (@p1316) :args (@t634)) % 0.41/0.81 (step @p1312 :rule eq_resolve :premises (@p1310 @p1307)) % 0.41/0.81 (step @p1313 :rule implies_elim :premises (@p1312)) % 0.41/0.81 (step @p1314 false :rule chain_m_resolution :premises (@p1313 @p1303 @p1289) :args (false (@list true false) (@list (or @t633 (= @t630 @t629)) @t352))) % 0.41/0.81 ) % 0.41/0.81 % SZS output end Proof % 0.41/0.81 % cvc5 exiting %------------------------------------------------------------------------------