%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 11:24:05 AM UTC 2026 % Result : Theorem 120.25s 151.19s % Output : Proof 150.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n004.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Fri Sep 4 20:18:44 UTC 2026 % 0.14/0.36 % CPUTime : % 0.14/0.44 %----Proving TH0 % 120.25/151.19 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 120.25/151.19 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 120.25/151.19 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 120.25/151.19 --- Run --ho-elim --full-saturate-quant at 18s... % 120.25/151.19 % SZS status Theorem % 120.25/151.19 % SZS output start Proof % 120.25/151.19 ( % 120.25/151.19 (declare-sort $$unsorted 0) % 120.25/151.19 (declare-sort tptp.mu 0) % 120.25/151.19 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 120.25/151.19 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 120.25/151.19 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 120.25/151.19 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 120.25/151.19 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 120.25/151.19 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 120.25/151.19 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 120.25/151.19 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 120.25/151.19 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 120.25/151.19 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 120.25/151.19 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 120.25/151.20 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 120.25/151.20 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 120.25/151.20 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 120.25/151.20 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 120.25/151.20 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 120.25/151.20 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 120.25/151.20 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 120.25/151.20 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 120.25/151.20 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 120.25/151.20 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 120.25/151.20 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 120.25/151.20 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 120.25/151.20 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 120.25/151.20 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 120.25/151.20 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 120.25/151.20 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 120.25/151.20 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 120.25/151.20 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 120.25/151.20 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 120.25/151.20 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 120.25/151.20 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 120.25/151.20 (define @t2 () (@var "__flatten_var_0" $$unsorted)) % 120.25/151.20 (define @t3 () (@var "Phi" (-> $$unsorted Bool))) % 120.25/151.20 (define @t4 () (_ tptp.mbox @t1)) % 120.25/151.20 (define @t5 () (_ tptp.mnot (_ @t4 @t3))) % 120.25/151.20 (define @t6 () (@list @t3 @t2)) % 120.25/151.20 (define @t7 () (lambda @t6 (_ (_ (_ tptp.mimplies @t5) (_ @t4 @t5)) @t2))) % 120.25/151.20 (define @t8 () (= (_ tptp.mvalid (_ tptp.mforall_prop @t7)) (_ tptp.meuclidean @t1))) % 120.25/151.20 (define @t9 () (@list @t1)) % 120.25/151.20 (define @t10 () (forall @t9 @t8)) % 120.25/151.20 (define @t11 () (not @t10)) % 120.25/151.20 (define @t12 () (@var "Y" tptp.mu)) % 120.25/151.20 (define @t13 () (@var "X" tptp.mu)) % 120.25/151.20 (define @t14 () (@var "W" $$unsorted)) % 120.25/151.20 (define @t15 () (lambda (@list @t13 @t12 @t14) (= @t13 @t12))) % 120.25/151.20 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 120.25/151.20 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 120.25/151.20 (define @t18 () (lambda (@list @t17 @t16 @t14) (= (_ @t17 @t14) (_ @t16 @t14)))) % 120.25/151.20 (define @t19 () (_ @t3 @t14)) % 120.25/151.20 (define @t20 () (not @t19)) % 120.25/151.20 (define @t21 () (@list @t3 @t14)) % 120.25/151.20 (define @t22 () (lambda @t21 @t20)) % 120.25/151.20 (define @t23 () (@var "Psi" (-> $$unsorted Bool))) % 120.25/151.20 (define @t24 () (_ @t23 @t14)) % 120.25/151.20 (define @t25 () (lambda (@list @t3 @t23 @t14) (or @t19 @t24))) % 120.25/151.20 (define @t26 () (_ tptp.mnot @t23)) % 120.25/151.20 (define @t27 () (_ tptp.mnot @t3)) % 120.25/151.20 (define @t28 () (_ tptp.mor @t27)) % 120.25/151.20 (define @t29 () (@list @t3 @t23 @t2)) % 120.25/151.20 (define @t30 () (lambda @t29 (_ (_ tptp.mnot (_ @t28 @t26)) @t2))) % 120.25/151.20 (define @t31 () (lambda @t29 (_ (_ @t28 @t23) @t2))) % 120.25/151.20 (define @t32 () (lambda @t29 (_ (_ (_ tptp.mor @t26) @t3) @t2))) % 120.25/151.20 (define @t33 () (lambda @t29 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t3) @t23)) (_ (_ tptp.mimplies @t23) @t3)) @t2))) % 120.25/151.20 (define @t34 () (lambda @t29 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t3) @t23)) @t2))) % 120.25/151.20 (define @t35 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 120.25/151.20 (define @t36 () (_ @t35 @t13)) % 120.25/151.20 (define @t37 () (lambda (@list @t35 @t14) (forall (@list @t13) (_ @t36 @t14)))) % 120.25/151.20 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 120.25/151.20 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 120.25/151.20 (define @t40 () (_ @t39 @t38)) % 120.25/151.20 (define @t41 () (_ @t40 @t14)) % 120.25/151.20 (define @t42 () (@list @t38)) % 120.25/151.20 (define @t43 () (forall @t42 @t41)) % 120.25/151.20 (define @t44 () (@list @t39 @t14)) % 120.25/151.20 (define @t45 () (lambda @t44 @t43)) % 120.25/151.20 (define @t46 () (lambda (@list @t35 @t2) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t13 @t2) (_ (_ tptp.mnot @t36) @t2)))) @t2))) % 120.25/151.20 (define @t47 () (lambda (@list @t39 @t2) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t2) (_ (_ tptp.mnot @t40) @t2)))) @t2))) % 120.25/151.20 (define @t48 () (@list @t14)) % 120.25/151.20 (define @t49 () (lambda @t48 true)) % 120.25/151.20 (define @t50 () (@var "V" $$unsorted)) % 120.25/151.20 (define @t51 () (_ @t3 @t50)) % 120.25/151.20 (define @t52 () (_ (_ @t1 @t14) @t50)) % 120.25/151.20 (define @t53 () (not @t52)) % 120.25/151.20 (define @t54 () (or @t53 @t51)) % 120.25/151.20 (define @t55 () (@list @t50)) % 120.25/151.20 (define @t56 () (forall @t55 @t54)) % 120.25/151.20 (define @t57 () (@list @t1 @t3 @t14)) % 120.25/151.20 (define @t58 () (lambda @t57 @t56)) % 120.25/151.20 (define @t59 () (lambda (@list @t1 @t3 @t2) (_ (_ tptp.mnot (_ @t4 @t27)) @t2))) % 120.25/151.20 (define @t60 () (@var "S" $$unsorted)) % 120.25/151.20 (define @t61 () (_ @t1 @t60)) % 120.25/151.20 (define @t62 () (@list @t60)) % 120.25/151.20 (define @t63 () (lambda @t9 (forall @t62 (_ @t61 @t60)))) % 120.25/151.20 (define @t64 () (@var "T" $$unsorted)) % 120.25/151.20 (define @t65 () (_ @t1 @t64)) % 120.25/151.20 (define @t66 () (_ @t61 @t64)) % 120.25/151.20 (define @t67 () (lambda @t9 (forall (@list @t60 @t64) (=> @t66 (_ @t65 @t60))))) % 120.25/151.20 (define @t68 () (@list @t64)) % 120.25/151.20 (define @t69 () (lambda @t9 (forall @t62 (exists @t68 @t66)))) % 120.25/151.20 (define @t70 () (@var "U" $$unsorted)) % 120.25/151.20 (define @t71 () (_ @t61 @t70)) % 120.25/151.20 (define @t72 () (_ @t65 @t70)) % 120.25/151.20 (define @t73 () (@list @t60 @t64 @t70)) % 120.25/151.20 (define @t74 () (lambda @t9 (forall @t73 (=> (and @t66 @t72) @t71)))) % 120.25/151.20 (define @t75 () (and @t66 @t71)) % 120.25/151.20 (define @t76 () (forall @t73 (=> @t75 @t72))) % 120.25/151.20 (define @t77 () (lambda @t9 @t76)) % 120.25/151.20 (define @t78 () (= @t64 @t70)) % 120.25/151.20 (define @t79 () (lambda @t9 (forall @t73 (=> @t75 @t78)))) % 120.25/151.20 (define @t80 () (@list @t70)) % 120.25/151.20 (define @t81 () (lambda @t9 (forall @t62 (exists @t68 (and @t66 (forall @t80 (=> @t71 @t78))))))) % 120.25/151.20 (define @t82 () (_ @t1 @t70)) % 120.25/151.20 (define @t83 () (_ @t82 @t64)) % 120.25/151.20 (define @t84 () (lambda @t9 (forall @t73 (=> @t66 (exists @t80 (and @t71 @t83)))))) % 120.25/151.20 (define @t85 () (lambda @t9 (forall @t73 (=> @t75 (or @t72 @t78 @t83))))) % 120.25/151.20 (define @t86 () (lambda @t9 (forall @t73 (=> @t75 (exists @t55 (and (_ @t65 @t50) (_ @t82 @t50))))))) % 120.25/151.20 (define @t87 () (forall @t48 @t19)) % 120.25/151.20 (define @t88 () (@list @t3)) % 120.25/151.20 (define @t89 () (lambda @t88 @t87)) % 120.25/151.20 (define @t90 () (lambda @t88 (forall @t48 @t20))) % 120.25/151.20 (define @t91 () (lambda @t88 (exists @t48 @t19))) % 120.25/151.20 (define @t92 () (lambda @t88 (exists @t48 @t20))) % 120.25/151.20 (define @t93 () (@var "BOUND_VARIABLE_8454" (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 120.25/151.20 (define @t94 () (@const 0 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 120.25/151.20 (define @t95 () (@const 1 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 120.25/151.20 (define @t96 () (_ @t94 @t93 @t60)) % 120.25/151.20 (define @t97 () (forall @t73 (or (not (_ @t95 @t96 @t64)) (not (_ @t95 @t96 @t70)) (_ @t95 (_ @t94 @t93 @t64) @t70)))) % 120.25/151.20 (define @t98 () (@var "BOUND_VARIABLE_8367" $$unsorted)) % 120.25/151.20 (define @t99 () (@var "BOUND_VARIABLE_8447" (@ho-elim-sort (-> $$unsorted Bool)))) % 120.25/151.20 (define @t100 () (_ @t95 @t99 @t98)) % 120.25/151.20 (define @t101 () (@var "BOUND_VARIABLE_8418" $$unsorted)) % 120.25/151.20 (define @t102 () (@list @t98)) % 120.25/151.20 (define @t103 () (_ @t94 @t93 @t14)) % 120.25/151.20 (define @t104 () (@var "BOUND_VARIABLE_8412" $$unsorted)) % 120.25/151.20 (define @t105 () (_ @t95 @t99 @t104)) % 120.25/151.20 (define @t106 () (@list @t14 @t99 @t104 @t101)) % 120.25/151.20 (define @t107 () (forall @t106 (or (not (_ @t95 @t103 @t104)) @t105 (not (_ @t95 @t103 @t101)) (not (forall @t102 (or (not (_ @t95 (_ @t94 @t93 @t101) @t98)) @t100)))))) % 120.25/151.20 (define @t108 () (@list @t93)) % 120.25/151.20 (define @t109 () (forall @t108 (= @t97 @t107))) % 120.25/151.20 (define @t110 () (not @t109)) % 120.25/151.20 (define @t111 () (_ @t38 @t98)) % 120.25/151.20 (define @t112 () (not (forall @t102 (or (not (_ @t1 @t101 @t98)) @t111)))) % 120.25/151.20 (define @t113 () (not (_ @t1 @t14 @t101))) % 120.25/151.20 (define @t114 () (_ @t38 @t104)) % 120.25/151.20 (define @t115 () (not (_ @t1 @t14 @t104))) % 120.25/151.20 (define @t116 () (or @t115 @t114 @t113 @t112)) % 120.25/151.20 (define @t117 () (forall (@list @t14 @t38 @t104 @t101) @t116)) % 120.25/151.20 (define @t118 () (_ @t1 @t64 @t70)) % 120.25/151.20 (define @t119 () (_ @t1 @t60 @t70)) % 120.25/151.20 (define @t120 () (_ @t1 @t60 @t64)) % 120.25/151.20 (define @t121 () (forall @t73 (or (not @t120) (not @t119) @t118))) % 120.25/151.20 (define @t122 () (@list @t38 @t104 @t101)) % 120.25/151.20 (define @t123 () (forall @t122 @t116)) % 120.25/151.20 (define @t124 () (lambda @t48 @t123)) % 120.25/151.20 (define @t125 () (_ @t124 @t14)) % 120.25/151.20 (define @t126 () (forall @t48 @t125)) % 120.25/151.20 (define @t127 () (_ @t3 @t14)) % 120.25/151.20 (define @t128 () (lambda @t88 (forall @t48 @t127))) % 120.25/151.20 (define @t129 () (or @t113 @t112)) % 120.25/151.20 (define @t130 () (or @t115 @t114)) % 120.25/151.20 (define @t131 () (or @t130 @t129)) % 120.25/151.20 (define @t132 () (forall @t122 @t131)) % 120.25/151.20 (define @t133 () (forall (@list @t104 @t101) @t131)) % 120.25/151.20 (define @t134 () (forall (@list @t101) @t129)) % 120.25/151.20 (define @t135 () (@list @t50)) % 120.25/151.20 (define @t136 () (forall (@list @t104) @t130)) % 120.25/151.20 (define @t137 () (or @t136 @t134)) % 120.25/151.20 (define @t138 () (not (_ @t1 @t50 @t98))) % 120.25/151.20 (define @t139 () (_ @t1 @t14 @t50)) % 120.25/151.20 (define @t140 () (not @t139)) % 120.25/151.20 (define @t141 () (or (forall @t55 (or @t140 (_ @t38 @t50))) (forall @t55 (or @t140 (not (forall @t102 (or @t138 @t111))))))) % 120.25/151.20 (define @t142 () (_ @t3 @t98)) % 120.25/151.20 (define @t143 () (not (forall @t102 (or @t138 @t142)))) % 120.25/151.20 (define @t144 () (not (_ @t1 @t2 @t50))) % 120.25/151.20 (define @t145 () (forall @t55 (or @t144 @t143))) % 120.25/151.20 (define @t146 () (_ @t3 @t50)) % 120.25/151.20 (define @t147 () (forall @t55 (or @t144 @t146))) % 120.25/151.20 (define @t148 () (or @t147 @t145)) % 120.25/151.20 (define @t149 () (lambda @t6 @t148)) % 120.25/151.20 (define @t150 () (_ @t149 @t38 @t14)) % 120.25/151.20 (define @t151 () (forall @t42 @t150)) % 120.25/151.20 (define @t152 () (lambda @t48 @t151)) % 120.25/151.20 (define @t153 () (_ @t39 @t38 @t14)) % 120.25/151.20 (define @t154 () (lambda @t44 (forall @t42 @t153))) % 120.25/151.20 (define @t155 () (@list @t2)) % 120.25/151.20 (define @t156 () (lambda @t48 (forall @t55 (or @t140 @t143)))) % 120.25/151.20 (define @t157 () (_ @t156 @t2)) % 120.25/151.20 (define @t158 () (or @t147 @t157)) % 120.25/151.20 (define @t159 () (lambda @t155 @t158)) % 120.25/151.20 (define @t160 () (_ @t23 @t2)) % 120.25/151.20 (define @t161 () (@list @t23 @t2)) % 120.25/151.20 (define @t162 () (forall @t55 (or @t140 @t146))) % 120.25/151.20 (define @t163 () (not @t162)) % 120.25/151.20 (define @t164 () (lambda @t48 @t163)) % 120.25/151.20 (define @t165 () (or @t140 (_ @t164 @t50))) % 120.25/151.20 (define @t166 () (forall @t55 @t165)) % 120.25/151.20 (define @t167 () (lambda @t48 @t166)) % 120.25/151.20 (define @t168 () (lambda @t21 @t162)) % 120.25/151.20 (define @t169 () (lambda @t48 @t162)) % 120.25/151.20 (define @t170 () (_ @t169 @t14)) % 120.25/151.20 (define @t171 () (not @t170)) % 120.25/151.20 (define @t172 () (lambda @t48 @t171)) % 120.25/151.20 (define @t173 () (_ (lambda @t57 @t162) @t1)) % 120.25/151.20 (define @t174 () (_ @t164 @t2)) % 120.25/151.20 (define @t175 () (not @t174)) % 120.25/151.20 (define @t176 () (or @t175 @t160)) % 120.25/151.20 (define @t177 () (lambda @t161 @t176)) % 120.25/151.20 (define @t178 () (or (not (_ @t3 @t2)) @t160)) % 120.25/151.20 (define @t179 () (lambda @t29 @t178)) % 120.25/151.20 (define @t180 () (_ @t22 (_ @t173 @t3))) % 120.25/151.20 (define @t181 () (lambda @t6 (_ (_ (_ @t179 @t180) (_ @t173 @t180)) @t2))) % 120.25/151.20 (define @t182 () (_ (lambda @t9 @t121) @t1)) % 120.25/151.20 (define @t183 () (_ @t128 (_ @t154 @t181))) % 120.25/151.20 (define @t184 () (forall @t9 (= @t183 @t182))) % 120.25/151.20 (define @t185 () (not @t71)) % 120.25/151.20 (define @t186 () (not @t66)) % 120.25/151.20 (define @t187 () (or @t186 @t185 @t72)) % 120.25/151.20 (define @t188 () (or @t20 @t24)) % 120.25/151.20 (define @t189 () (lambda @t48 @t188)) % 120.25/151.20 (define @t190 () (@list @t23 @t14)) % 120.25/151.20 (define @t191 () (lambda @t48 @t20)) % 120.25/151.20 (define @t192 () (_ @t191 @t14)) % 120.25/151.20 (define @t193 () (or @t192 @t24)) % 120.25/151.20 (define @t194 () (lambda @t190 @t193)) % 120.25/151.20 (define @t195 () (@quantifiers_skolemize (forall @t108 (= @t107 @t97)) 0)) % 120.25/151.20 (define @t196 () (_ @t94 @t195 @t60)) % 120.25/151.20 (define @t197 () (forall @t73 (or (not (_ @t95 @t196 @t64)) (not (_ @t95 @t196 @t70)) (_ @t95 (_ @t94 @t195 @t64) @t70)))) % 120.25/151.20 (define @t198 () (_ @t94 @t195 @t14)) % 120.25/151.20 (define @t199 () (forall @t106 (or (not (_ @t95 @t198 @t104)) @t105 (not (_ @t95 @t198 @t101)) (not (forall @t102 (or (not (_ @t95 (_ @t94 @t195 @t101) @t98)) @t100)))))) % 120.25/151.20 (define @t200 () (= @t199 @t197)) % 120.25/151.20 (define @t201 () (@quantifiers_skolemize @t197 2)) % 120.25/151.20 (define @t202 () (@quantifiers_skolemize @t197 1)) % 120.25/151.20 (define @t203 () (_ @t94 @t195 @t202)) % 120.25/151.20 (define @t204 () (_ @t95 @t203 @t201)) % 120.25/151.20 (define @t205 () (@quantifiers_skolemize @t197 0)) % 120.25/151.20 (define @t206 () (_ @t94 @t195 @t205)) % 120.25/151.20 (define @t207 () (_ @t95 @t206 @t201)) % 120.25/151.20 (define @t208 () (not @t207)) % 120.25/151.20 (define @t209 () (_ @t95 @t206 @t202)) % 120.25/151.20 (define @t210 () (not @t209)) % 120.25/151.20 (define @t211 () (or @t210 @t208 @t204)) % 120.25/151.20 (define @t212 () (not @t211)) % 120.25/151.20 (define @t213 () (not @t197)) % 120.25/151.20 (define @t214 () (or @t208 @t204 @t210)) % 120.25/151.20 (define @t215 () (_ @t95 @t203 @t98)) % 120.25/151.20 (define @t216 () (forall @t102 (or (not @t215) @t215))) % 120.25/151.20 (define @t217 () (not @t216)) % 120.25/151.20 (define @t218 () (or @t208 @t204 @t210 @t217)) % 120.25/151.20 (define @t219 () (not @t199)) % 120.25/151.20 (define @t220 () (@quantifiers_skolemize @t199 1)) % 120.25/151.20 (define @t221 () (@quantifiers_skolemize @t199 3)) % 120.25/151.20 (define @t222 () (_ @t94 @t195 @t221)) % 120.25/151.20 (define @t223 () (forall @t102 (or (not (_ @t95 @t222 @t98)) (_ @t95 @t220 @t98)))) % 120.25/151.20 (define @t224 () (not @t223)) % 120.25/151.20 (define @t225 () (@quantifiers_skolemize @t199 0)) % 120.25/151.20 (define @t226 () (_ @t94 @t195 @t225)) % 120.25/151.20 (define @t227 () (_ @t95 @t226 @t221)) % 120.25/151.20 (define @t228 () (not @t227)) % 120.25/151.20 (define @t229 () (@quantifiers_skolemize @t199 2)) % 120.25/151.20 (define @t230 () (_ @t95 @t220 @t229)) % 120.25/151.20 (define @t231 () (_ @t95 @t226 @t229)) % 120.25/151.20 (define @t232 () (not @t231)) % 120.25/151.20 (define @t233 () (or @t232 @t230 @t228 @t224)) % 120.25/151.20 (define @t234 () (not @t233)) % 120.25/151.20 (define @t235 () (@list true)) % 120.25/151.20 (define @t236 () (@list @t233)) % 120.25/151.20 (define @t237 () (_ @t95 @t222 @t229)) % 120.25/151.20 (define @t238 () (not @t237)) % 120.25/151.20 (define @t239 () (or @t238 @t230)) % 120.25/151.20 (define @t240 () (@list true false)) % 120.25/151.20 (define @t241 () (or @t228 @t232 @t237)) % 120.25/151.20 (define @t242 () (not @t241)) % 120.25/151.20 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 120.25/151.20 (assume @p2 @t11) % 120.25/151.20 (assume @p3 true) % 120.25/151.20 (step @p4 (= tptp.meq_ind @t15) :rule refl :args (@t15)) % 120.25/151.20 (step @p5 (= tptp.meq_prop @t18) :rule refl :args (@t18)) % 120.25/151.20 (step @p6 (= tptp.mnot @t22) :rule refl :args (@t22)) % 120.25/151.20 (step @p7 (= tptp.mor @t25) :rule refl :args (@t25)) % 120.25/151.20 (step @p8 (= tptp.mand @t30) :rule refl :args (@t30)) % 120.25/151.20 (step @p9 (= tptp.mimplies @t31) :rule refl :args (@t31)) % 120.25/151.20 (step @p10 (= tptp.mimplied @t32) :rule refl :args (@t32)) % 120.25/151.20 (step @p11 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 120.25/151.20 (step @p12 (= tptp.mxor @t34) :rule refl :args (@t34)) % 120.25/151.20 (step @p13 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 120.25/151.20 (step @p14 (= tptp.mforall_prop @t45) :rule refl :args (@t45)) % 120.25/151.20 (step @p15 (= tptp.mexists_ind @t46) :rule refl :args (@t46)) % 120.25/151.20 (step @p16 (= tptp.mexists_prop @t47) :rule refl :args (@t47)) % 120.25/151.20 (step @p17 (= tptp.mtrue @t49) :rule refl :args (@t49)) % 120.25/151.20 (step @p18 (= tptp.mbox @t58) :rule refl :args (@t58)) % 120.25/151.20 (step @p19 (= tptp.mdia @t59) :rule refl :args (@t59)) % 120.25/151.20 (step @p20 (= tptp.mreflexive @t63) :rule refl :args (@t63)) % 120.25/151.20 (step @p21 (= tptp.msymmetric @t67) :rule refl :args (@t67)) % 120.25/151.20 (step @p22 (= tptp.mserial @t69) :rule refl :args (@t69)) % 120.25/151.20 (step @p23 (= tptp.mtransitive @t74) :rule refl :args (@t74)) % 120.25/151.20 (step @p24 (= tptp.meuclidean @t77) :rule refl :args (@t77)) % 120.25/151.20 (step @p25 (= tptp.mpartially_functional @t79) :rule refl :args (@t79)) % 120.25/151.20 (step @p26 (= tptp.mfunctional @t81) :rule refl :args (@t81)) % 120.25/151.20 (step @p27 (= tptp.mweakly_dense @t84) :rule refl :args (@t84)) % 120.25/151.20 (step @p28 (= tptp.mweakly_connected @t85) :rule refl :args (@t85)) % 120.25/151.20 (step @p29 (= tptp.mweakly_directed @t86) :rule refl :args (@t86)) % 120.25/151.20 (step @p30 (= tptp.mvalid @t89) :rule refl :args (@t89)) % 120.25/151.20 (step @p31 (= tptp.minvalid @t90) :rule refl :args (@t90)) % 120.25/151.20 (step @p32 (= tptp.msatisfiable @t91) :rule refl :args (@t91)) % 120.25/151.20 (step @p33 (= tptp.mcountersatisfiable @t92) :rule refl :args (@t92)) % 120.25/151.20 (step @p34 :rule eq-symm :args (@t97 @t107)) % 120.25/151.20 (step @p35 :rule cong :premises (@p34) :args (@t109)) % 120.25/151.20 (step @p36 :rule cong :premises (@p35) :args (@t110)) % 120.25/151.20 ; WARNING: add trust step for TRUST % 120.25/151.20 ; trust TRUST PREPROCESS_HO_ELIM % 120.25/151.20 (step @p37 :rule trust :premises () :args ((= (not (forall @t9 (= @t121 @t117))) @t110))) % 120.25/151.20 (step @p38 :rule quant-merge-prenex :args ((= (forall @t48 @t123) @t117))) % 120.25/151.20 (step @p39 :rule beta-reduce :args ((= @t125 @t123))) % 120.25/151.20 (step @p40 :rule cong :premises (@p39) :args (@t126)) % 120.25/151.20 (step @p41 :rule trans :premises (@p40 @p38)) % 120.25/151.20 (step @p42 :rule beta-reduce :args ((= (_ @t128 @t124) @t126))) % 120.25/151.20 (step @p43 :rule trans :premises (@p42 @p41)) % 120.25/151.20 (step @p44 :rule aci_norm :args ((= @t131 @t116))) % 120.25/151.20 (step @p45 :rule cong :premises (@p44) :args (@t132)) % 120.25/151.20 (step @p46 :rule quant-merge-prenex :args ((= (forall @t42 @t133) @t132))) % 120.25/151.20 (step @p47 :rule alpha_equiv :args (@t134 (@list @t101) @t135)) % 120.25/151.20 (step @p48 :rule alpha_equiv :args (@t136 (@list @t104) @t135)) % 120.25/151.20 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t137)) % 120.25/151.20 (step @p50 :rule quant-miniscope-or :args ((= @t133 @t137))) % 120.25/151.20 (step @p51 :rule trans :premises (@p50 @p49)) % 120.25/151.20 (step @p52 :rule symm :premises (@p51)) % 120.25/151.20 (step @p53 :rule cong :premises (@p52) :args ((forall @t42 @t141))) % 120.25/151.20 (step @p54 :rule trans :premises (@p53 @p46)) % 120.25/151.20 (step @p55 :rule trans :premises (@p54 @p45)) % 120.25/151.20 (step @p56 :rule beta-reduce :args ((= @t150 @t141))) % 120.25/151.20 (step @p57 :rule cong :premises (@p56) :args (@t151)) % 120.25/151.20 (step @p58 :rule trans :premises (@p57 @p55)) % 120.25/151.20 (step @p59 :rule cong :premises (@p58) :args (@t152)) % 120.25/151.20 (step @p60 :rule beta-reduce :args ((= (_ @t154 @t149) @t152))) % 120.25/151.20 (step @p61 :rule trans :premises (@p60 @p59)) % 120.25/151.20 (step @p62 :rule beta-reduce :args ((= (_ (lambda @t155 @t148) @t2) @t148))) % 120.25/151.20 (step @p63 :rule refl :args (@t2)) % 120.25/151.20 (step @p64 :rule beta-reduce :args ((= @t157 @t145))) % 120.25/151.20 (step @p65 :rule refl :args (@t147)) % 120.25/151.20 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t158)) % 120.25/151.20 (step @p67 :rule cong :premises (@p66) :args (@t159)) % 120.25/151.20 (step @p68 :rule beta-reduce :args ((= (_ (lambda @t161 (or @t147 @t160)) @t156) @t159))) % 120.25/151.20 (step @p69 :rule trans :premises (@p68 @p67)) % 120.25/151.20 (step @p70 :rule beta-reduce :args ((= (_ (lambda @t48 (not (forall @t102 (or (not (_ @t1 @t14 @t98)) @t142)))) @t50) @t143))) % 120.25/151.20 (step @p71 :rule refl :args (@t50)) % 120.25/151.20 (step @p72 :rule alpha_equiv :args (@t162 @t135 (@list @t98))) % 120.25/151.20 (step @p73 :rule cong :premises (@p72) :args (@t163)) % 120.25/151.20 (step @p74 :rule cong :premises (@p73) :args (@t164)) % 120.25/151.20 (step @p75 :rule ho_cong :premises (@p74 @p71)) % 120.25/151.20 (step @p76 :rule trans :premises (@p75 @p70)) % 120.25/151.20 (step @p77 :rule refl :args (@t140)) % 120.25/151.20 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t165)) % 120.25/151.20 (step @p79 :rule cong :premises (@p78) :args (@t166)) % 120.25/151.20 (step @p80 :rule cong :premises (@p79) :args (@t167)) % 120.25/151.20 (step @p81 :rule beta-reduce :args ((= (_ @t168 @t164) @t167))) % 120.25/151.20 (step @p82 :rule trans :premises (@p81 @p80)) % 120.25/151.20 (step @p83 :rule beta-reduce :args ((= @t170 @t162))) % 120.25/151.20 (step @p84 :rule cong :premises (@p83) :args (@t171)) % 120.25/151.20 (step @p85 :rule cong :premises (@p84) :args (@t172)) % 120.25/151.20 (step @p86 :rule beta-reduce :args ((= (_ @t22 @t169) @t172))) % 120.25/151.20 (step @p87 :rule trans :premises (@p86 @p85)) % 120.25/151.20 (step @p88 :rule beta-reduce :args ((= (_ @t168 @t3) @t169))) % 120.25/151.20 (step @p89 :rule refl :args (@t3)) % 120.25/151.20 (step @p90 :rule beta-reduce :args ((= @t173 @t168))) % 120.25/151.20 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 120.25/151.20 (step @p92 :rule trans :premises (@p91 @p88)) % 120.25/151.20 (step @p93 :rule refl :args (@t22)) % 120.25/151.20 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 120.25/151.20 (step @p95 :rule trans :premises (@p94 @p87)) % 120.25/151.20 (step @p96 :rule ho_cong :premises (@p90 @p95)) % 120.25/151.20 (step @p97 :rule trans :premises (@p96 @p82)) % 120.25/151.20 (step @p98 :rule refl :args (@t160)) % 120.25/151.20 (step @p99 :rule bool-double-not-elim :args (@t147)) % 120.25/151.20 (step @p100 :rule beta-reduce :args ((= @t174 (not @t147)))) % 120.25/151.20 (step @p101 :rule cong :premises (@p100) :args (@t175)) % 120.25/151.20 (step @p102 :rule trans :premises (@p101 @p99)) % 120.25/151.20 (step @p103 :rule nary_cong :premises (@p102 @p98) :args (@t176)) % 120.25/151.20 (step @p104 :rule cong :premises (@p103) :args (@t177)) % 120.25/151.20 (step @p105 :rule beta-reduce :args ((= (_ @t179 @t164) @t177))) % 120.25/151.20 (step @p106 :rule trans :premises (@p105 @p104)) % 120.25/151.20 (step @p107 :rule refl :args (@t179)) % 120.25/151.20 (step @p108 :rule ho_cong :premises (@p107 @p95)) % 120.25/151.20 (step @p109 :rule trans :premises (@p108 @p106)) % 120.25/151.20 (step @p110 :rule ho_cong :premises (@p109 @p97)) % 120.25/151.20 (step @p111 :rule trans :premises (@p110 @p69)) % 120.25/151.20 (step @p112 :rule ho_cong :premises (@p111 @p63)) % 120.25/151.20 (step @p113 :rule trans :premises (@p112 @p62)) % 120.25/151.20 (step @p114 :rule cong :premises (@p113) :args (@t181)) % 120.25/151.20 (step @p115 :rule refl :args (@t154)) % 120.25/151.20 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 120.25/151.20 (step @p117 :rule trans :premises (@p116 @p61)) % 120.25/151.20 (step @p118 :rule refl :args (@t128)) % 120.25/151.20 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 120.25/151.20 (step @p120 :rule trans :premises (@p119 @p43)) % 120.25/151.20 (step @p121 :rule beta-reduce :args ((= @t182 @t121))) % 120.25/151.20 (step @p122 :rule cong :premises (@p121 @p120) :args ((= @t182 @t183))) % 120.25/151.20 (step @p123 :rule eq-symm :args (@t183 @t182)) % 120.25/151.20 (step @p124 :rule trans :premises (@p123 @p122)) % 120.25/151.20 (step @p125 :rule cong :premises (@p124) :args (@t184)) % 120.25/151.20 (step @p126 :rule cong :premises (@p125) :args ((not @t184))) % 120.25/151.20 (step @p127 :rule refl :args (@t1)) % 120.25/151.20 (step @p128 :rule refl :args (@t118)) % 120.25/151.20 (step @p129 :rule refl :args (@t72)) % 120.25/151.20 (step @p130 :rule cong :premises (@p129 @p128) :args ((= @t72 @t118))) % 120.25/151.20 (step @p131 :rule symm :premises (@p130)) % 120.25/151.20 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 120.25/151.20 (step @p133 :rule refl :args (@t119)) % 120.25/151.20 (step @p134 :rule refl :args (@t71)) % 120.25/151.20 (step @p135 :rule cong :premises (@p134 @p133) :args ((= @t71 @t119))) % 120.25/151.20 (step @p136 :rule symm :premises (@p135)) % 120.25/151.20 (step @p137 :rule eq_resolve :premises (@p134 @p136)) % 120.25/151.20 (step @p138 :rule cong :premises (@p137) :args (@t185)) % 120.25/151.20 (step @p139 :rule refl :args (@t120)) % 120.25/151.20 (step @p140 :rule refl :args (@t66)) % 120.25/151.20 (step @p141 :rule cong :premises (@p140 @p139) :args ((= @t66 @t120))) % 120.25/151.20 (step @p142 :rule symm :premises (@p141)) % 120.25/151.20 (step @p143 :rule eq_resolve :premises (@p140 @p142)) % 120.25/151.20 (step @p144 :rule cong :premises (@p143) :args (@t186)) % 120.25/151.20 (step @p145 :rule nary_cong :premises (@p144 @p138 @p132) :args (@t187)) % 120.25/151.20 (step @p146 :rule cong :premises (@p145) :args ((forall @t73 @t187))) % 120.25/151.20 (step @p147 :rule aci_norm :args ((= (or (or @t186 @t185) @t72) @t187))) % 120.25/151.20 (step @p148 :rule bool-and-de-morgan :args (@t66 @t71 true)) % 120.25/151.20 (step @p149 :rule nary_cong :premises (@p148 @p129) :args ((or (not @t75) @t72))) % 120.25/151.20 (step @p150 :rule trans :premises (@p149 @p147)) % 120.25/151.20 (step @p151 :rule bool-impl-elim :args (@t75 @t72)) % 120.25/151.20 (step @p152 :rule trans :premises (@p151 @p150)) % 120.25/151.20 (step @p153 :rule cong :premises (@p152) :args (@t76)) % 120.25/151.20 (step @p154 :rule trans :premises (@p153 @p146)) % 120.25/151.20 (step @p155 :rule cong :premises (@p154) :args (@t77)) % 120.25/151.20 (step @p156 :rule trans :premises (@p24 @p155)) % 120.25/151.20 (step @p157 :rule ho_cong :premises (@p156 @p127)) % 120.25/151.20 (step @p158 :rule refl :args (@t146)) % 120.25/151.20 (step @p159 :rule refl :args (@t51)) % 120.25/151.20 (step @p160 :rule cong :premises (@p159 @p158) :args ((= @t51 @t146))) % 120.25/151.20 (step @p161 :rule symm :premises (@p160)) % 120.25/151.20 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 120.25/151.20 (step @p163 :rule refl :args (@t139)) % 120.25/151.20 (step @p164 :rule refl :args (@t52)) % 120.25/151.20 (step @p165 :rule cong :premises (@p164 @p163) :args ((= @t52 @t139))) % 120.25/151.20 (step @p166 :rule symm :premises (@p165)) % 120.25/151.20 (step @p167 :rule eq_resolve :premises (@p164 @p166)) % 120.25/151.20 (step @p168 :rule cong :premises (@p167) :args (@t53)) % 120.25/151.20 (step @p169 :rule nary_cong :premises (@p168 @p162) :args (@t54)) % 150.36/151.20 (step @p170 :rule cong :premises (@p169) :args (@t56)) % 150.36/151.20 (step @p171 :rule cong :premises (@p170) :args (@t58)) % 150.36/151.20 (step @p172 :rule trans :premises (@p18 @p171)) % 150.36/151.20 (step @p173 :rule ho_cong :premises (@p172 @p127)) % 150.36/151.20 (step @p174 :rule ho_cong :premises (@p173 @p89)) % 150.36/151.20 (step @p175 :rule ho_cong :premises (@p6 @p174)) % 150.36/151.20 (step @p176 :rule ho_cong :premises (@p173 @p175)) % 150.36/151.20 (step @p177 :rule beta-reduce :args ((= (_ @t189 @t2) @t178))) % 150.36/151.20 (step @p178 :rule beta-reduce :args ((= (_ (lambda @t190 @t188) @t23) @t189))) % 150.36/151.20 (step @p179 :rule refl :args (@t23)) % 150.36/151.20 (step @p180 :rule refl :args (@t24)) % 150.36/151.20 (step @p181 :rule beta-reduce :args ((= @t192 @t20))) % 150.36/151.20 (step @p182 :rule nary_cong :premises (@p181 @p180) :args (@t193)) % 150.36/151.20 (step @p183 :rule cong :premises (@p182) :args (@t194)) % 150.36/151.20 (step @p184 :rule beta-reduce :args ((= (_ @t25 @t191) @t194))) % 150.36/151.20 (step @p185 :rule trans :premises (@p184 @p183)) % 150.36/151.20 (step @p186 :rule beta-reduce :args ((= (_ @t22 @t3) @t191))) % 150.36/151.20 (step @p187 :rule refl :args (@t25)) % 150.36/151.20 (step @p188 :rule ho_cong :premises (@p187 @p186)) % 150.36/151.20 (step @p189 :rule trans :premises (@p188 @p185)) % 150.36/151.20 (step @p190 :rule ho_cong :premises (@p189 @p179)) % 150.36/151.20 (step @p191 :rule trans :premises (@p190 @p178)) % 150.36/151.20 (step @p192 :rule ho_cong :premises (@p191 @p63)) % 150.36/151.20 (step @p193 :rule trans :premises (@p192 @p177)) % 150.36/151.20 (step @p194 :rule ho_cong :premises (@p6 @p89)) % 150.36/151.20 (step @p195 :rule ho_cong :premises (@p7 @p194)) % 150.36/151.20 (step @p196 :rule ho_cong :premises (@p195 @p179)) % 150.36/151.20 (step @p197 :rule ho_cong :premises (@p196 @p63)) % 150.36/151.20 (step @p198 :rule trans :premises (@p197 @p193)) % 150.36/151.20 (step @p199 :rule cong :premises (@p198) :args (@t31)) % 150.36/151.20 (step @p200 :rule trans :premises (@p9 @p199)) % 150.36/151.20 (step @p201 :rule ho_cong :premises (@p200 @p175)) % 150.36/151.20 (step @p202 :rule ho_cong :premises (@p201 @p176)) % 150.36/151.20 (step @p203 :rule ho_cong :premises (@p202 @p63)) % 150.36/151.20 (step @p204 :rule cong :premises (@p203) :args (@t7)) % 150.36/151.20 (step @p205 :rule refl :args (@t153)) % 150.36/151.20 (step @p206 :rule refl :args (@t41)) % 150.36/151.20 (step @p207 :rule cong :premises (@p206 @p205) :args ((= @t41 @t153))) % 150.36/151.20 (step @p208 :rule symm :premises (@p207)) % 150.36/151.20 (step @p209 :rule eq_resolve :premises (@p206 @p208)) % 150.36/151.20 (step @p210 :rule cong :premises (@p209) :args (@t43)) % 150.36/151.20 (step @p211 :rule cong :premises (@p210) :args (@t45)) % 150.36/151.20 (step @p212 :rule trans :premises (@p14 @p211)) % 150.36/151.20 (step @p213 :rule ho_cong :premises (@p212 @p204)) % 150.36/151.20 (step @p214 :rule refl :args (@t127)) % 150.36/151.20 (step @p215 :rule refl :args (@t19)) % 150.36/151.20 (step @p216 :rule cong :premises (@p215 @p214) :args ((= @t19 @t127))) % 150.36/151.20 (step @p217 :rule symm :premises (@p216)) % 150.36/151.20 (step @p218 :rule eq_resolve :premises (@p215 @p217)) % 150.36/151.20 (step @p219 :rule cong :premises (@p218) :args (@t87)) % 150.36/151.20 (step @p220 :rule cong :premises (@p219) :args (@t89)) % 150.36/151.20 (step @p221 :rule trans :premises (@p30 @p220)) % 150.36/151.20 (step @p222 :rule ho_cong :premises (@p221 @p213)) % 150.36/151.20 (step @p223 :rule cong :premises (@p222 @p157) :args (@t8)) % 150.36/151.20 (step @p224 :rule cong :premises (@p223) :args (@t10)) % 150.36/151.20 (step @p225 :rule cong :premises (@p224) :args (@t11)) % 150.36/151.20 (step @p226 :rule trans :premises (@p225 @p126)) % 150.36/151.20 (step @p227 :rule trans :premises (@p226 @p37 @p36)) % 150.36/151.20 (step @p228 :rule eq_resolve :premises (@p2 @p227)) % 150.36/151.20 (step @p229 :rule skolemize :premises (@p228)) % 150.36/151.20 (step @p230 :rule cnf_equiv_neg2 :args (@t200)) % 150.36/151.20 (step @p231 :rule refl :args (@t212)) % 150.36/151.20 (step @p232 :rule bool-double-not-elim :args (@t197)) % 150.36/151.20 (step @p233 :rule nary_cong :premises (@p232 @p231) :args ((or (not @t213) @t212))) % 150.36/151.20 (assume-push @p328 @t213) % 150.36/151.20 (step @p235 :rule skolemize :premises (@p328)) % 150.36/151.20 (step-pop @p329 :rule scope :premises (@p235)) % 150.36/151.20 (step @p236 :rule process_scope :premises (@p329) :args (@t212)) % 150.36/151.20 (step @p238 :rule implies_elim :premises (@p236)) % 150.36/151.20 (step @p239 :rule eq_resolve :premises (@p238 @p233)) % 150.36/151.20 (step @p240 :rule bool-double-not-elim :args (@t209)) % 150.36/151.20 (step @p241 :rule refl :args (@t211)) % 150.36/151.20 (step @p242 :rule nary_cong :premises (@p241 @p240) :args ((or @t211 (not @t210)))) % 150.36/151.20 (step @p243 :rule cnf_or_neg :args (@t211 0)) % 150.36/151.20 (step @p244 :rule eq_resolve :premises (@p243 @p242)) % 150.36/151.20 (step @p245 :rule reordering :premises (@p244) :args ((or @t209 @t211))) % 150.36/151.20 (step @p246 :rule bool-double-not-elim :args (@t207)) % 150.36/151.20 (step @p247 :rule nary_cong :premises (@p241 @p246) :args ((or @t211 (not @t208)))) % 150.36/151.20 (step @p248 :rule cnf_or_neg :args (@t211 1)) % 150.36/151.20 (step @p249 :rule eq_resolve :premises (@p248 @p247)) % 150.36/151.20 (step @p250 :rule reordering :premises (@p249) :args ((or @t207 @t211))) % 150.36/151.20 (step @p251 :rule cnf_or_neg :args (@t211 2)) % 150.36/151.20 (step @p252 :rule cnf_or_pos :args (@t214)) % 150.36/151.20 (step @p253 :rule reordering :premises (@p252) :args ((or @t210 @t208 @t204 (not @t214)))) % 150.36/151.20 (step @p254 :rule aci_norm :args ((= (or @t208 @t204 @t210 false) @t214))) % 150.36/151.20 (step @p255 :rule evaluate :args ((not true))) % 150.36/151.20 (step @p256 :rule quant-unused-vars :args ((= (forall @t102 true) true))) % 150.36/151.20 (step @p257 :rule bool-or-taut2 :args (false @t215 false false)) % 150.36/151.20 (step @p258 :rule cong :premises (@p257) :args (@t216)) % 150.36/151.20 (step @p259 :rule trans :premises (@p258 @p256)) % 150.36/151.20 (step @p260 :rule cong :premises (@p259) :args (@t217)) % 150.36/151.20 (step @p261 :rule trans :premises (@p260 @p255)) % 150.36/151.20 (step @p262 :rule refl :args (@t210)) % 150.36/151.20 (step @p263 :rule refl :args (@t204)) % 150.36/151.20 (step @p264 :rule refl :args (@t208)) % 150.36/151.20 (step @p265 :rule nary_cong :premises (@p264 @p263 @p262 @p261) :args (@t218)) % 150.36/151.20 (step @p266 :rule trans :premises (@p265 @p254)) % 150.36/151.20 (step @p267 :rule refl :args (@t199)) % 150.36/151.20 (step @p268 :rule cong :premises (@p267 @p266) :args ((=> @t199 @t218))) % 150.36/151.20 (assume-push @p330 @t199) % 150.36/151.20 (step @p270 :rule instantiate :premises (@p330) :args ((@list @t205 @t203 @t201 @t202))) % 150.36/151.20 (step-pop @p331 :rule scope :premises (@p270)) % 150.36/151.20 (step @p271 :rule process_scope :premises (@p331) :args (@t218)) % 150.36/151.20 (step @p273 :rule eq_resolve :premises (@p271 @p268)) % 150.36/151.20 (step @p274 :rule implies_elim :premises (@p273)) % 150.36/151.20 (step @p275 :rule chain_m_resolution :premises (@p274 @p253 @p251 @p250 @p245 @p239 @p230 @p229) :args (@t219 (@list true true false false true true true) (@list @t214 @t204 @t207 @t209 @t211 @t197 @t200))) % 150.36/151.20 (step @p276 :rule cnf_equiv_neg1 :args (@t200)) % 150.36/151.20 (step @p277 :rule reordering :premises (@p276) :args ((or @t199 @t197 @t200))) % 150.36/151.20 (step @p278 :rule chain_m_resolution :premises (@p277 @p275 @p229) :args (@t197 (@list true true) (@list @t199 @t200))) % 150.36/151.20 (step @p279 :rule refl :args (@t234)) % 150.36/151.20 (step @p280 :rule bool-double-not-elim :args (@t199)) % 150.36/151.20 (step @p281 :rule nary_cong :premises (@p280 @p279) :args ((or (not @t219) @t234))) % 150.36/151.20 (assume-push @p332 @t219) % 150.36/151.20 (step @p283 :rule skolemize :premises (@p332)) % 150.36/151.20 (step-pop @p333 :rule scope :premises (@p283)) % 150.36/151.20 (step @p284 :rule process_scope :premises (@p333) :args (@t234)) % 150.36/151.20 (step @p286 :rule implies_elim :premises (@p284)) % 150.36/151.20 (step @p287 :rule eq_resolve :premises (@p286 @p281)) % 150.36/151.20 (step @p288 :rule chain_m_resolution :premises (@p287 @p275) :args (@t234 @t235 (@list @t199))) % 150.36/151.20 (step @p289 :rule bool-double-not-elim :args (@t223)) % 150.36/151.20 (step @p290 :rule refl :args (@t233)) % 150.36/151.20 (step @p291 :rule nary_cong :premises (@p290 @p289) :args ((or @t233 (not @t224)))) % 150.36/151.20 (step @p292 :rule cnf_or_neg :args (@t233 3)) % 150.36/151.20 (step @p293 :rule eq_resolve :premises (@p292 @p291)) % 150.36/151.20 (step @p294 :rule reordering :premises (@p293) :args ((or @t223 @t233))) % 150.36/151.20 (step @p295 :rule chain_m_resolution :premises (@p294 @p288) :args (@t223 @t235 @t236)) % 150.36/151.20 (assume-push @p334 @t223) % 150.36/151.20 (step @p297 :rule instantiate :premises (@p334) :args ((@list @t229))) % 150.36/151.20 (step-pop @p335 :rule scope :premises (@p297)) % 150.36/151.20 (step @p298 :rule process_scope :premises (@p335) :args (@t239)) % 150.36/151.20 (step @p300 :rule implies_elim :premises (@p298)) % 150.36/151.20 (step @p301 :rule chain_m_resolution :premises (@p300 @p295) :args (@t239 (@list false) (@list @t223))) % 150.36/151.20 (step @p302 :rule cnf_or_neg :args (@t233 1)) % 150.36/151.20 (step @p303 :rule chain_m_resolution :premises (@p302 @p288) :args ((not @t230) @t235 @t236)) % 150.36/151.20 (step @p304 :rule cnf_or_pos :args (@t239)) % 150.36/151.20 (step @p305 :rule reordering :premises (@p304) :args ((or @t230 @t238 (not @t239)))) % 150.36/151.20 (step @p306 :rule chain_m_resolution :premises (@p305 @p303 @p301) :args (@t238 @t240 (@list @t230 @t239))) % 150.36/151.20 (step @p307 :rule bool-double-not-elim :args (@t227)) % 150.36/151.20 (step @p308 :rule nary_cong :premises (@p290 @p307) :args ((or @t233 (not @t228)))) % 150.36/151.20 (step @p309 :rule cnf_or_neg :args (@t233 2)) % 150.36/151.20 (step @p310 :rule eq_resolve :premises (@p309 @p308)) % 150.36/151.20 (step @p311 :rule reordering :premises (@p310) :args ((or @t227 @t233))) % 150.36/151.20 (step @p312 :rule chain_m_resolution :premises (@p311 @p288) :args (@t227 @t235 @t236)) % 150.36/151.20 (step @p313 :rule bool-double-not-elim :args (@t231)) % 150.36/151.20 (step @p314 :rule nary_cong :premises (@p290 @p313) :args ((or @t233 (not @t232)))) % 150.36/151.20 (step @p315 :rule cnf_or_neg :args (@t233 0)) % 150.36/151.20 (step @p316 :rule eq_resolve :premises (@p315 @p314)) % 150.36/151.20 (step @p317 :rule reordering :premises (@p316) :args ((or @t231 @t233))) % 150.36/151.20 (step @p318 :rule chain_m_resolution :premises (@p317 @p288) :args (@t231 @t235 @t236)) % 150.36/151.20 (step @p319 :rule cnf_or_pos :args (@t241)) % 150.36/151.20 (step @p320 :rule reordering :premises (@p319) :args ((or @t232 @t228 @t237 @t242))) % 150.36/151.20 (step @p321 :rule chain_m_resolution :premises (@p320 @p318 @p312 @p306) :args (@t242 (@list false false true) (@list @t231 @t227 @t237))) % 150.36/151.20 (assume-push @p336 @t197) % 150.36/151.20 (step @p323 :rule instantiate :premises (@p336) :args ((@list @t225 @t221 @t229))) % 150.36/151.20 (step-pop @p337 :rule scope :premises (@p323)) % 150.36/151.20 (step @p324 :rule process_scope :premises (@p337) :args (@t241)) % 150.36/151.20 (step @p326 :rule implies_elim :premises (@p324)) % 150.36/151.20 (step @p327 false :rule chain_m_resolution :premises (@p326 @p321 @p278) :args (false @t240 (@list @t241 @t197))) % 150.36/151.20 ) % 150.36/151.20 % SZS output end Proof % 150.36/151.20 % cvc5 exiting %------------------------------------------------------------------------------