%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : AGT028^2 : TPTP v9.2.1. Released 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 : n012.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 08:04:47 AM UTC 2026 % Result : Theorem 0.51s 0.74s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : AGT028^2 : TPTP v9.2.1. Released v5.2.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Wed Jun 3 01:32:48 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.34 %----Proving TH0 % 0.51/0.74 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.51/0.74 % SZS status Theorem % 0.51/0.74 % SZS output start Proof % 0.51/0.74 ( % 0.51/0.74 (declare-sort $$unsorted 0) % 0.51/0.74 (declare-sort tptp.mu 0) % 0.51/0.74 (declare-const tptp.mike tptp.mu) % 0.51/0.74 (declare-const tptp.peter tptp.mu) % 0.51/0.74 (declare-const tptp.tom tptp.mu) % 0.51/0.74 (declare-const tptp.john tptp.mu) % 0.51/0.74 (declare-const tptp.physics_student (-> tptp.mu $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.good_in_physics (-> tptp.mu $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.mathematician (-> tptp.mu $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.good_in_maths (-> tptp.mu $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.r4 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.maths_teacher (-> tptp.mu $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.r1 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.r5 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.r3 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.maths_student (-> tptp.mu $$unsorted Bool)) % 0.51/0.74 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.51/0.74 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.51/0.74 (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)))))) % 0.51/0.74 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.51/0.74 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.51/0.74 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.51/0.74 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.51/0.74 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.51/0.74 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.51/0.74 (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))))))) % 0.51/0.74 (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))))))) % 0.51/0.74 (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)))))) % 0.51/0.74 (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)))))) % 0.51/0.74 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.51/0.74 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.51/0.74 (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)))))) % 0.51/0.74 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.51/0.74 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.51/0.74 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.51/0.74 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.51/0.74 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.51/0.74 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.51/0.74 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.51/0.74 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.51/0.74 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.51/0.74 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.51/0.74 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.51/0.74 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.51/0.74 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.51/0.74 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.51/0.74 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.51/0.74 (define @t2 () (@var "X" tptp.mu)) % 0.51/0.74 (define @t3 () (_ tptp.good_in_maths @t2)) % 0.51/0.74 (define @t4 () (_ tptp.mbox tptp.r4)) % 0.51/0.74 (define @t5 () (_ @t4 @t3)) % 0.51/0.74 (define @t6 () (_ tptp.maths_teacher @t2)) % 0.51/0.74 (define @t7 () (@list @t2 @t1)) % 0.51/0.74 (define @t8 () (lambda @t7 (_ (_ (_ tptp.mimplies @t6) @t5) @t1))) % 0.51/0.74 (define @t9 () (_ tptp.mbox tptp.r1)) % 0.51/0.74 (define @t10 () (_ tptp.mathematician @t2)) % 0.51/0.74 (define @t11 () (_ tptp.mbox tptp.r5)) % 0.51/0.74 (define @t12 () (_ tptp.mbox tptp.r2)) % 0.51/0.74 (define @t13 () (_ tptp.mbox tptp.r3)) % 0.51/0.74 (define @t14 () (_ tptp.mdia tptp.r1)) % 0.51/0.74 (define @t15 () (_ tptp.mimplies (_ tptp.maths_student @t2))) % 0.51/0.74 (define @t16 () (_ tptp.mdia tptp.r2)) % 0.51/0.74 (define @t17 () (_ @t16 @t3)) % 0.51/0.74 (define @t18 () (_ tptp.mdia tptp.r3)) % 0.51/0.74 (define @t19 () (_ tptp.mdia tptp.r4)) % 0.51/0.74 (define @t20 () (_ tptp.mdia tptp.r5)) % 0.51/0.74 (define @t21 () (_ tptp.good_in_physics @t2)) % 0.51/0.74 (define @t22 () (_ tptp.mimplies (_ tptp.physics_student @t2))) % 0.51/0.74 (define @t23 () (_ tptp.maths_teacher tptp.john)) % 0.51/0.74 (define @t24 () (lambda @t7 (_ @t5 @t1))) % 0.51/0.74 (define @t25 () (not (_ tptp.mvalid (_ tptp.mexists_ind @t24)))) % 0.51/0.74 (define @t26 () (@var "Y" tptp.mu)) % 0.51/0.74 (define @t27 () (@var "W" $$unsorted)) % 0.51/0.74 (define @t28 () (lambda (@list @t2 @t26 @t27) (= @t2 @t26))) % 0.51/0.74 (define @t29 () (@var "Y" (-> $$unsorted Bool))) % 0.51/0.74 (define @t30 () (@var "X" (-> $$unsorted Bool))) % 0.51/0.74 (define @t31 () (lambda (@list @t30 @t29 @t27) (= (_ @t30 @t27) (_ @t29 @t27)))) % 0.51/0.74 (define @t32 () (@var "Phi" (-> $$unsorted Bool))) % 0.51/0.74 (define @t33 () (_ @t32 @t27)) % 0.51/0.74 (define @t34 () (not @t33)) % 0.51/0.74 (define @t35 () (@list @t32 @t27)) % 0.51/0.74 (define @t36 () (lambda @t35 @t34)) % 0.51/0.74 (define @t37 () (@var "Psi" (-> $$unsorted Bool))) % 0.51/0.74 (define @t38 () (_ @t37 @t27)) % 0.51/0.74 (define @t39 () (lambda (@list @t32 @t37 @t27) (or @t33 @t38))) % 0.51/0.74 (define @t40 () (_ tptp.mnot @t37)) % 0.51/0.74 (define @t41 () (_ tptp.mnot @t32)) % 0.51/0.74 (define @t42 () (_ tptp.mor @t41)) % 0.51/0.74 (define @t43 () (@list @t32 @t37 @t1)) % 0.51/0.74 (define @t44 () (lambda @t43 (_ (_ tptp.mnot (_ @t42 @t40)) @t1))) % 0.51/0.74 (define @t45 () (lambda @t43 (_ (_ @t42 @t37) @t1))) % 0.51/0.74 (define @t46 () (lambda @t43 (_ (_ (_ tptp.mor @t40) @t32) @t1))) % 0.51/0.74 (define @t47 () (lambda @t43 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t32) @t37)) (_ (_ tptp.mimplies @t37) @t32)) @t1))) % 0.51/0.74 (define @t48 () (lambda @t43 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t32) @t37)) @t1))) % 0.51/0.74 (define @t49 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.51/0.74 (define @t50 () (_ @t49 @t2)) % 0.51/0.74 (define @t51 () (_ @t50 @t27)) % 0.51/0.74 (define @t52 () (@list @t2)) % 0.51/0.74 (define @t53 () (forall @t52 @t51)) % 0.51/0.74 (define @t54 () (@list @t49 @t27)) % 0.51/0.74 (define @t55 () (lambda @t54 @t53)) % 0.51/0.74 (define @t56 () (@var "P" (-> $$unsorted Bool))) % 0.51/0.74 (define @t57 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.51/0.74 (define @t58 () (_ @t57 @t56)) % 0.51/0.74 (define @t59 () (lambda (@list @t57 @t27) (forall (@list @t56) (_ @t58 @t27)))) % 0.51/0.74 (define @t60 () (lambda @t7 (_ (_ tptp.mnot @t50) @t1))) % 0.51/0.74 (define @t61 () (@list @t49 @t1)) % 0.51/0.74 (define @t62 () (lambda @t61 (_ (_ tptp.mnot (_ tptp.mforall_ind @t60)) @t1))) % 0.51/0.74 (define @t63 () (lambda (@list @t57 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t56 @t1) (_ (_ tptp.mnot @t58) @t1)))) @t1))) % 0.51/0.74 (define @t64 () (@list @t27)) % 0.51/0.74 (define @t65 () (lambda @t64 true)) % 0.51/0.74 (define @t66 () (@var "V" $$unsorted)) % 0.51/0.74 (define @t67 () (_ @t32 @t66)) % 0.51/0.74 (define @t68 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.51/0.74 (define @t69 () (_ (_ @t68 @t27) @t66)) % 0.51/0.74 (define @t70 () (not @t69)) % 0.51/0.74 (define @t71 () (or @t70 @t67)) % 0.51/0.74 (define @t72 () (@list @t66)) % 0.51/0.74 (define @t73 () (forall @t72 @t71)) % 0.51/0.74 (define @t74 () (@list @t68 @t32 @t27)) % 0.51/0.74 (define @t75 () (lambda @t74 @t73)) % 0.51/0.74 (define @t76 () (lambda (@list @t68 @t32 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t68) @t41)) @t1))) % 0.51/0.74 (define @t77 () (@var "S" $$unsorted)) % 0.51/0.74 (define @t78 () (_ @t68 @t77)) % 0.51/0.74 (define @t79 () (@list @t77)) % 0.51/0.74 (define @t80 () (@list @t68)) % 0.51/0.74 (define @t81 () (lambda @t80 (forall @t79 (_ @t78 @t77)))) % 0.51/0.74 (define @t82 () (@var "T" $$unsorted)) % 0.51/0.74 (define @t83 () (_ @t68 @t82)) % 0.51/0.74 (define @t84 () (_ @t78 @t82)) % 0.51/0.74 (define @t85 () (lambda @t80 (forall (@list @t77 @t82) (=> @t84 (_ @t83 @t77))))) % 0.51/0.74 (define @t86 () (@list @t82)) % 0.51/0.74 (define @t87 () (lambda @t80 (forall @t79 (exists @t86 @t84)))) % 0.51/0.74 (define @t88 () (@var "U" $$unsorted)) % 0.51/0.74 (define @t89 () (_ @t78 @t88)) % 0.51/0.74 (define @t90 () (_ @t83 @t88)) % 0.51/0.74 (define @t91 () (@list @t77 @t82 @t88)) % 0.51/0.74 (define @t92 () (lambda @t80 (forall @t91 (=> (and @t84 @t90) @t89)))) % 0.51/0.74 (define @t93 () (and @t84 @t89)) % 0.51/0.74 (define @t94 () (lambda @t80 (forall @t91 (=> @t93 @t90)))) % 0.51/0.74 (define @t95 () (= @t82 @t88)) % 0.51/0.74 (define @t96 () (lambda @t80 (forall @t91 (=> @t93 @t95)))) % 0.51/0.74 (define @t97 () (@list @t88)) % 0.51/0.74 (define @t98 () (lambda @t80 (forall @t79 (exists @t86 (and @t84 (forall @t97 (=> @t89 @t95))))))) % 0.51/0.74 (define @t99 () (_ @t68 @t88)) % 0.51/0.74 (define @t100 () (_ @t99 @t82)) % 0.51/0.74 (define @t101 () (lambda @t80 (forall @t91 (=> @t84 (exists @t97 (and @t89 @t100)))))) % 0.51/0.74 (define @t102 () (lambda @t80 (forall @t91 (=> @t93 (or @t90 @t95 @t100))))) % 0.51/0.74 (define @t103 () (lambda @t80 (forall @t91 (=> @t93 (exists @t72 (and (_ @t83 @t66) (_ @t99 @t66))))))) % 0.51/0.74 (define @t104 () (forall @t64 @t33)) % 0.51/0.74 (define @t105 () (@list @t32)) % 0.51/0.74 (define @t106 () (lambda @t105 @t104)) % 0.51/0.74 (define @t107 () (lambda @t105 (forall @t64 @t34))) % 0.51/0.74 (define @t108 () (lambda @t105 (exists @t64 @t33))) % 0.51/0.74 (define @t109 () (lambda @t105 (exists @t64 @t34))) % 0.51/0.74 (define @t110 () (@var "BOUND_VARIABLE_8548" $$unsorted)) % 0.51/0.74 (define @t111 () (tptp.good_in_maths @t2 @t110)) % 0.51/0.74 (define @t112 () (not (tptp.r4 @t27 @t110))) % 0.51/0.74 (define @t113 () (tptp.maths_teacher @t2 @t27)) % 0.51/0.74 (define @t114 () (not @t113)) % 0.51/0.74 (define @t115 () (or @t114 @t112 @t111)) % 0.51/0.74 (define @t116 () (forall (@list @t27 @t2 @t110) @t115)) % 0.51/0.74 (define @t117 () (@list @t2 @t110)) % 0.51/0.74 (define @t118 () (forall @t117 @t115)) % 0.51/0.74 (define @t119 () (lambda @t64 @t118)) % 0.51/0.74 (define @t120 () (_ @t119 @t27)) % 0.51/0.74 (define @t121 () (forall @t64 @t120)) % 0.51/0.74 (define @t122 () (_ @t32 @t27)) % 0.51/0.74 (define @t123 () (lambda @t105 (forall @t64 @t122))) % 0.51/0.74 (define @t124 () (or @t112 @t111)) % 0.51/0.74 (define @t125 () (or @t114 @t124)) % 0.51/0.74 (define @t126 () (forall @t117 @t125)) % 0.51/0.74 (define @t127 () (@list @t110)) % 0.51/0.74 (define @t128 () (forall @t127 @t125)) % 0.51/0.74 (define @t129 () (forall @t127 @t124)) % 0.51/0.74 (define @t130 () (or @t114 @t129)) % 0.51/0.74 (define @t131 () (tptp.good_in_maths @t2 @t66)) % 0.51/0.74 (define @t132 () (not (tptp.r4 @t27 @t66))) % 0.51/0.74 (define @t133 () (forall @t72 (or @t132 @t131))) % 0.51/0.74 (define @t134 () (_ @t6 @t27)) % 0.51/0.74 (define @t135 () (not @t134)) % 0.51/0.74 (define @t136 () (or @t135 @t133)) % 0.51/0.74 (define @t137 () (forall @t72 (or (not (tptp.r4 @t1 @t66)) @t131))) % 0.51/0.74 (define @t138 () (not (_ @t6 @t1))) % 0.51/0.74 (define @t139 () (or @t138 @t137)) % 0.51/0.74 (define @t140 () (lambda @t7 @t139)) % 0.51/0.74 (define @t141 () (_ @t140 @t2 @t27)) % 0.51/0.74 (define @t142 () (forall @t52 @t141)) % 0.51/0.74 (define @t143 () (lambda @t64 @t142)) % 0.51/0.74 (define @t144 () (_ @t49 @t2 @t27)) % 0.51/0.74 (define @t145 () (lambda @t54 (forall @t52 @t144))) % 0.51/0.74 (define @t146 () (@list @t1)) % 0.51/0.74 (define @t147 () (lambda @t64 @t133)) % 0.51/0.74 (define @t148 () (_ @t147 @t1)) % 0.51/0.74 (define @t149 () (or @t138 @t148)) % 0.51/0.74 (define @t150 () (lambda @t146 @t149)) % 0.51/0.74 (define @t151 () (_ @t37 @t1)) % 0.51/0.74 (define @t152 () (lambda (@list @t37 @t1) (or @t138 @t151))) % 0.51/0.74 (define @t153 () (_ @t3 @t66)) % 0.51/0.74 (define @t154 () (or @t132 @t153)) % 0.51/0.74 (define @t155 () (_ @t3 @t66)) % 0.51/0.74 (define @t156 () (or @t132 @t155)) % 0.51/0.74 (define @t157 () (forall @t72 @t156)) % 0.51/0.74 (define @t158 () (lambda @t64 @t157)) % 0.51/0.74 (define @t159 () (_ @t32 @t66)) % 0.51/0.74 (define @t160 () (lambda @t35 (forall @t72 (or @t132 @t159)))) % 0.51/0.74 (define @t161 () (_ @t68 @t27 @t66)) % 0.51/0.74 (define @t162 () (_ (lambda @t74 (forall @t72 (or (not @t161) @t159))) tptp.r4)) % 0.51/0.74 (define @t163 () (or (not (_ @t32 @t1)) @t151)) % 0.51/0.74 (define @t164 () (_ (lambda @t43 @t163) @t6)) % 0.51/0.74 (define @t165 () (_ @t162 @t3)) % 0.51/0.74 (define @t166 () (or @t34 @t38)) % 0.51/0.74 (define @t167 () (lambda @t64 @t166)) % 0.51/0.74 (define @t168 () (@list @t37 @t27)) % 0.51/0.74 (define @t169 () (lambda @t64 @t34)) % 0.51/0.74 (define @t170 () (_ @t169 @t27)) % 0.51/0.74 (define @t171 () (or @t170 @t38)) % 0.51/0.74 (define @t172 () (lambda @t168 @t171)) % 0.51/0.74 (define @t173 () (not (forall @t52 (not @t133)))) % 0.51/0.74 (define @t174 () (lambda @t146 (not (forall @t52 (not @t137))))) % 0.51/0.74 (define @t175 () (_ @t174 @t27)) % 0.51/0.74 (define @t176 () (forall @t64 @t175)) % 0.51/0.74 (define @t177 () (lambda @t7 @t137)) % 0.51/0.74 (define @t178 () (_ @t177 @t2 @t1)) % 0.51/0.74 (define @t179 () (not @t178)) % 0.51/0.74 (define @t180 () (forall @t52 @t179)) % 0.51/0.74 (define @t181 () (not @t180)) % 0.51/0.74 (define @t182 () (lambda @t146 @t181)) % 0.51/0.74 (define @t183 () (not (forall @t52 (not (_ @t49 @t2 @t1))))) % 0.51/0.74 (define @t184 () (lambda @t61 @t183)) % 0.51/0.74 (define @t185 () (lambda @t7 (_ @t165 @t1))) % 0.51/0.74 (define @t186 () (forall @t52 (not @t144))) % 0.51/0.74 (define @t187 () (lambda @t64 @t186)) % 0.51/0.74 (define @t188 () (_ @t187 @t27)) % 0.51/0.74 (define @t189 () (not @t188)) % 0.51/0.74 (define @t190 () (lambda @t64 @t189)) % 0.51/0.74 (define @t191 () (not @t51)) % 0.51/0.74 (define @t192 () (not (_ @t50 @t1))) % 0.51/0.74 (define @t193 () (lambda @t7 @t192)) % 0.51/0.74 (define @t194 () (_ @t193 @t2 @t27)) % 0.51/0.74 (define @t195 () (forall @t52 @t194)) % 0.51/0.74 (define @t196 () (lambda @t64 @t195)) % 0.51/0.74 (define @t197 () (lambda @t64 @t191)) % 0.51/0.74 (define @t198 () (_ @t36 @t50)) % 0.51/0.74 (define @t199 () (forall @t64 @t173)) % 0.51/0.74 (define @t200 () (@quantifiers_skolemize @t199 0)) % 0.51/0.74 (define @t201 () (not (tptp.r4 @t200 @t66))) % 0.51/0.74 (define @t202 () (forall @t52 (not (forall @t72 (or @t201 @t131))))) % 0.51/0.74 (define @t203 () (not @t199)) % 0.51/0.74 (define @t204 () (not (not @t202))) % 0.51/0.74 (define @t205 () (@list true)) % 0.51/0.74 (define @t206 () (@quantifiers_skolemize (forall @t72 (or @t201 (tptp.good_in_maths tptp.john @t66))) 0)) % 0.51/0.74 (define @t207 () (tptp.good_in_maths tptp.john @t206)) % 0.51/0.74 (define @t208 () (tptp.r4 @t200 @t206)) % 0.51/0.74 (define @t209 () (not @t208)) % 0.51/0.74 (define @t210 () (or @t209 @t207)) % 0.51/0.74 (define @t211 () (@list @t210)) % 0.51/0.74 (define @t212 () (tptp.maths_teacher tptp.john @t27)) % 0.51/0.74 (define @t213 () (_ @t23 @t27)) % 0.51/0.74 (define @t214 () (_ @t23 @t27)) % 0.51/0.74 (define @t215 () (forall @t64 @t214)) % 0.51/0.74 (define @t216 () (tptp.maths_teacher tptp.john @t200)) % 0.51/0.74 (define @t217 () (not @t216)) % 0.51/0.74 (define @t218 () (or @t217 @t209 @t207)) % 0.51/0.74 (define @t219 () (not @t218)) % 0.51/0.74 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.51/0.74 (assume @p2 (_ tptp.mvalid (_ tptp.mforall_ind @t8))) % 0.51/0.74 (assume @p3 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t11 (_ (_ tptp.mimplies (_ @t9 @t10)) (_ @t9 @t3))) @t1))))) % 0.51/0.74 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t11 (_ (_ tptp.mimplies (_ @t12 @t10)) (_ @t12 @t3))) @t1))))) % 0.51/0.74 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t11 (_ (_ tptp.mimplies (_ @t13 @t10)) (_ @t13 @t3))) @t1))))) % 0.51/0.74 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t11 (_ (_ tptp.mimplies (_ @t4 @t10)) @t5)) @t1))))) % 0.51/0.74 (assume @p7 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t11 (_ (_ tptp.mimplies (_ @t11 @t10)) (_ @t11 @t3))) @t1))))) % 0.51/0.74 (assume @p8 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t15 (_ @t14 @t3))) @t1))))) % 0.51/0.74 (assume @p9 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t15 @t17)) @t1))))) % 0.51/0.74 (assume @p10 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t15 (_ @t18 @t3))) @t1))))) % 0.51/0.74 (assume @p11 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t15 (_ @t19 @t3))) @t1))))) % 0.51/0.74 (assume @p12 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t15 (_ @t20 @t3))) @t1))))) % 0.51/0.74 (assume @p13 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t22 (_ @t14 @t21))) @t1))))) % 0.51/0.74 (assume @p14 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t22 (_ @t16 @t21))) @t1))))) % 0.51/0.74 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t22 (_ @t18 @t21))) @t1))))) % 0.51/0.74 (assume @p16 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t22 (_ @t19 @t21))) @t1))))) % 0.51/0.74 (assume @p17 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t13 (_ @t22 (_ @t20 @t21))) @t1))))) % 0.51/0.74 (assume @p18 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t7 (_ (_ @t12 (_ (_ tptp.mimplies @t21) @t17)) @t1))))) % 0.51/0.74 (assume @p19 (_ tptp.mvalid @t23)) % 0.51/0.74 (assume @p20 (_ tptp.mvalid (_ @t12 (_ tptp.mathematician tptp.tom)))) % 0.51/0.74 (assume @p21 (_ tptp.mvalid (_ @t11 (_ tptp.maths_student tptp.peter)))) % 0.51/0.74 (assume @p22 (_ tptp.mvalid (_ @t11 (_ tptp.physics_student tptp.mike)))) % 0.51/0.74 (assume @p23 @t25) % 0.51/0.74 (assume @p24 true) % 0.51/0.74 (step @p25 (= tptp.meq_ind @t28) :rule refl :args (@t28)) % 0.51/0.74 (step @p26 (= tptp.meq_prop @t31) :rule refl :args (@t31)) % 0.51/0.74 (step @p27 (= tptp.mnot @t36) :rule refl :args (@t36)) % 0.51/0.74 (step @p28 (= tptp.mor @t39) :rule refl :args (@t39)) % 0.51/0.74 (step @p29 (= tptp.mand @t44) :rule refl :args (@t44)) % 0.51/0.74 (step @p30 (= tptp.mimplies @t45) :rule refl :args (@t45)) % 0.51/0.74 (step @p31 (= tptp.mimplied @t46) :rule refl :args (@t46)) % 0.51/0.74 (step @p32 (= tptp.mequiv @t47) :rule refl :args (@t47)) % 0.51/0.74 (step @p33 (= tptp.mxor @t48) :rule refl :args (@t48)) % 0.51/0.74 (step @p34 (= tptp.mforall_ind @t55) :rule refl :args (@t55)) % 0.51/0.74 (step @p35 (= tptp.mforall_prop @t59) :rule refl :args (@t59)) % 0.51/0.74 (step @p36 (= tptp.mexists_ind @t62) :rule refl :args (@t62)) % 0.51/0.74 (step @p37 (= tptp.mexists_prop @t63) :rule refl :args (@t63)) % 0.51/0.74 (step @p38 (= tptp.mtrue @t65) :rule refl :args (@t65)) % 0.51/0.74 (step @p39 (= tptp.mbox @t75) :rule refl :args (@t75)) % 0.51/0.74 (step @p40 (= tptp.mdia @t76) :rule refl :args (@t76)) % 0.51/0.74 (step @p41 (= tptp.mreflexive @t81) :rule refl :args (@t81)) % 0.51/0.74 (step @p42 (= tptp.msymmetric @t85) :rule refl :args (@t85)) % 0.51/0.74 (step @p43 (= tptp.mserial @t87) :rule refl :args (@t87)) % 0.51/0.74 (step @p44 (= tptp.mtransitive @t92) :rule refl :args (@t92)) % 0.51/0.74 (step @p45 (= tptp.meuclidean @t94) :rule refl :args (@t94)) % 0.51/0.74 (step @p46 (= tptp.mpartially_functional @t96) :rule refl :args (@t96)) % 0.51/0.74 (step @p47 (= tptp.mfunctional @t98) :rule refl :args (@t98)) % 0.51/0.74 (step @p48 (= tptp.mweakly_dense @t101) :rule refl :args (@t101)) % 0.51/0.74 (step @p49 (= tptp.mweakly_connected @t102) :rule refl :args (@t102)) % 0.51/0.74 (step @p50 (= tptp.mweakly_directed @t103) :rule refl :args (@t103)) % 0.51/0.74 (step @p51 (= tptp.mvalid @t106) :rule refl :args (@t106)) % 0.51/0.74 (step @p52 (= tptp.minvalid @t107) :rule refl :args (@t107)) % 0.51/0.74 (step @p53 (= tptp.msatisfiable @t108) :rule refl :args (@t108)) % 0.51/0.74 (step @p54 (= tptp.mcountersatisfiable @t109) :rule refl :args (@t109)) % 0.51/0.74 (step @p55 :rule quant-merge-prenex :args ((= (forall @t64 @t118) @t116))) % 0.51/0.74 (step @p56 :rule beta-reduce :args ((= @t120 @t118))) % 0.51/0.74 (step @p57 :rule cong :premises (@p56) :args (@t121)) % 0.51/0.74 (step @p58 :rule trans :premises (@p57 @p55)) % 0.51/0.74 (step @p59 :rule beta-reduce :args ((= (_ @t123 @t119) @t121))) % 0.51/0.74 (step @p60 :rule trans :premises (@p59 @p58)) % 0.51/0.74 (step @p61 :rule aci_norm :args ((= @t125 @t115))) % 0.51/0.74 (step @p62 :rule cong :premises (@p61) :args (@t126)) % 0.51/0.74 (step @p63 :rule quant-merge-prenex :args ((= (forall @t52 @t128) @t126))) % 0.51/0.74 (step @p64 :rule alpha_equiv :args (@t129 (@list @t110) (@list @t66))) % 0.51/0.74 (step @p65 :rule refl :args (@t114)) % 0.51/0.74 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t130)) % 0.51/0.74 (step @p67 :rule quant-miniscope-or :args ((= @t128 @t130))) % 0.51/0.74 (step @p68 :rule trans :premises (@p67 @p66)) % 0.51/0.74 (step @p69 :rule symm :premises (@p68)) % 0.51/0.74 (step @p70 :rule cong :premises (@p69) :args ((forall @t52 (or @t114 @t133)))) % 0.51/0.74 (step @p71 :rule trans :premises (@p70 @p63)) % 0.51/0.74 (step @p72 :rule trans :premises (@p71 @p62)) % 0.51/0.74 (step @p73 :rule refl :args (@t133)) % 0.51/0.74 (step @p74 :rule refl :args (@t113)) % 0.51/0.74 (step @p75 :rule refl :args (@t134)) % 0.51/0.74 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t134 @t113))) % 0.51/0.74 (step @p77 :rule symm :premises (@p76)) % 0.51/0.74 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.51/0.74 (step @p79 :rule cong :premises (@p78) :args (@t135)) % 0.51/0.74 (step @p80 :rule nary_cong :premises (@p79 @p73) :args (@t136)) % 0.51/0.74 (step @p81 :rule cong :premises (@p80) :args ((forall @t52 @t136))) % 0.51/0.74 (step @p82 :rule trans :premises (@p81 @p72)) % 0.51/0.74 (step @p83 :rule beta-reduce :args ((= @t141 @t136))) % 0.51/0.74 (step @p84 :rule cong :premises (@p83) :args (@t142)) % 0.51/0.74 (step @p85 :rule trans :premises (@p84 @p82)) % 0.51/0.74 (step @p86 :rule cong :premises (@p85) :args (@t143)) % 0.51/0.74 (step @p87 :rule beta-reduce :args ((= (_ @t145 @t140) @t143))) % 0.51/0.74 (step @p88 :rule trans :premises (@p87 @p86)) % 0.51/0.74 (step @p89 :rule beta-reduce :args ((= (_ (lambda @t146 @t139) @t1) @t139))) % 0.51/0.74 (step @p90 :rule refl :args (@t1)) % 0.51/0.74 (step @p91 :rule beta-reduce :args ((= @t148 @t137))) % 0.51/0.74 (step @p92 :rule refl :args (@t138)) % 0.51/0.74 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t149)) % 0.51/0.74 (step @p94 :rule cong :premises (@p93) :args (@t150)) % 0.51/0.74 (step @p95 :rule beta-reduce :args ((= (_ @t152 @t147) @t150))) % 0.51/0.74 (step @p96 :rule trans :premises (@p95 @p94)) % 0.51/0.74 (step @p97 :rule refl :args (@t131)) % 0.51/0.74 (step @p98 :rule refl :args (@t153)) % 0.51/0.74 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t153 @t131))) % 0.51/0.74 (step @p100 :rule symm :premises (@p99)) % 0.51/0.74 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.51/0.74 (step @p102 :rule refl :args (@t132)) % 0.51/0.74 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t154)) % 0.51/0.74 (step @p104 :rule cong :premises (@p103) :args ((forall @t72 @t154))) % 0.51/0.74 (step @p105 :rule refl :args (@t155)) % 0.51/0.74 (step @p106 :rule refl :args (@t132)) % 0.51/0.74 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t156)) % 0.51/0.74 (step @p108 :rule cong :premises (@p107) :args (@t157)) % 0.51/0.74 (step @p109 :rule trans :premises (@p108 @p104)) % 0.51/0.74 (step @p110 :rule cong :premises (@p109) :args (@t158)) % 0.51/0.74 (step @p111 :rule beta-reduce :args ((= (_ @t160 @t3) @t158))) % 0.51/0.74 (step @p112 :rule trans :premises (@p111 @p110)) % 0.51/0.74 (step @p113 :rule refl :args (@t3)) % 0.51/0.74 (step @p114 :rule beta-reduce :args ((= @t162 @t160))) % 0.51/0.74 (step @p115 :rule ho_cong :premises (@p114 @p113)) % 0.51/0.74 (step @p116 :rule trans :premises (@p115 @p112)) % 0.51/0.74 (step @p117 :rule beta-reduce :args ((= @t164 @t152))) % 0.51/0.74 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.51/0.74 (step @p119 :rule trans :premises (@p118 @p96)) % 0.51/0.74 (step @p120 :rule ho_cong :premises (@p119 @p90)) % 0.51/0.74 (step @p121 :rule trans :premises (@p120 @p89)) % 0.51/0.74 (step @p122 :rule cong :premises (@p121) :args ((lambda @t7 (_ (_ @t164 @t165) @t1)))) % 0.51/0.74 (step @p123 :rule refl :args (@t145)) % 0.51/0.74 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.51/0.74 (step @p125 :rule trans :premises (@p124 @p88)) % 0.51/0.74 (step @p126 :rule refl :args (@t123)) % 0.51/0.74 (step @p127 :rule ho_cong :premises (@p126 @p125)) % 0.51/0.74 (step @p128 :rule trans :premises (@p127 @p60)) % 0.51/0.74 (step @p129 :rule refl :args (tptp.r4)) % 0.51/0.74 (step @p130 :rule refl :args (@t159)) % 0.51/0.74 (step @p131 :rule refl :args (@t67)) % 0.51/0.74 (step @p132 :rule cong :premises (@p131 @p130) :args ((= @t67 @t159))) % 0.51/0.74 (step @p133 :rule symm :premises (@p132)) % 0.51/0.74 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 0.51/0.74 (step @p135 :rule refl :args (@t161)) % 0.51/0.74 (step @p136 :rule refl :args (@t69)) % 0.51/0.74 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t69 @t161))) % 0.51/0.74 (step @p138 :rule symm :premises (@p137)) % 0.51/0.74 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.51/0.74 (step @p140 :rule cong :premises (@p139) :args (@t70)) % 0.51/0.74 (step @p141 :rule nary_cong :premises (@p140 @p134) :args (@t71)) % 0.51/0.74 (step @p142 :rule cong :premises (@p141) :args (@t73)) % 0.51/0.74 (step @p143 :rule cong :premises (@p142) :args (@t75)) % 0.51/0.74 (step @p144 :rule trans :premises (@p39 @p143)) % 0.51/0.74 (step @p145 :rule ho_cong :premises (@p144 @p129)) % 0.51/0.74 (step @p146 :rule ho_cong :premises (@p145 @p113)) % 0.51/0.74 (step @p147 :rule refl :args (@t6)) % 0.51/0.74 (step @p148 :rule beta-reduce :args ((= (_ @t167 @t1) @t163))) % 0.51/0.74 (step @p149 :rule beta-reduce :args ((= (_ (lambda @t168 @t166) @t37) @t167))) % 0.51/0.74 (step @p150 :rule refl :args (@t37)) % 0.51/0.74 (step @p151 :rule refl :args (@t38)) % 0.51/0.74 (step @p152 :rule beta-reduce :args ((= @t170 @t34))) % 0.51/0.74 (step @p153 :rule nary_cong :premises (@p152 @p151) :args (@t171)) % 0.51/0.74 (step @p154 :rule cong :premises (@p153) :args (@t172)) % 0.51/0.74 (step @p155 :rule beta-reduce :args ((= (_ @t39 @t169) @t172))) % 0.51/0.74 (step @p156 :rule trans :premises (@p155 @p154)) % 0.51/0.74 (step @p157 :rule beta-reduce :args ((= (_ @t36 @t32) @t169))) % 0.51/0.74 (step @p158 :rule refl :args (@t39)) % 0.51/0.74 (step @p159 :rule ho_cong :premises (@p158 @p157)) % 0.51/0.74 (step @p160 :rule trans :premises (@p159 @p156)) % 0.51/0.74 (step @p161 :rule ho_cong :premises (@p160 @p150)) % 0.51/0.74 (step @p162 :rule trans :premises (@p161 @p149)) % 0.51/0.74 (step @p163 :rule ho_cong :premises (@p162 @p90)) % 0.51/0.74 (step @p164 :rule trans :premises (@p163 @p148)) % 0.51/0.74 (step @p165 :rule refl :args (@t32)) % 0.51/0.74 (step @p166 :rule ho_cong :premises (@p27 @p165)) % 0.51/0.74 (step @p167 :rule ho_cong :premises (@p28 @p166)) % 0.51/0.74 (step @p168 :rule ho_cong :premises (@p167 @p150)) % 0.51/0.74 (step @p169 :rule ho_cong :premises (@p168 @p90)) % 0.51/0.74 (step @p170 :rule trans :premises (@p169 @p164)) % 0.51/0.74 (step @p171 :rule cong :premises (@p170) :args (@t45)) % 0.51/0.74 (step @p172 :rule trans :premises (@p30 @p171)) % 0.51/0.74 (step @p173 :rule ho_cong :premises (@p172 @p147)) % 0.51/0.74 (step @p174 :rule ho_cong :premises (@p173 @p146)) % 0.51/0.74 (step @p175 :rule ho_cong :premises (@p174 @p90)) % 0.51/0.74 (step @p176 :rule cong :premises (@p175) :args (@t8)) % 0.51/0.74 (step @p177 :rule refl :args (@t144)) % 0.51/0.74 (step @p178 :rule refl :args (@t51)) % 0.51/0.74 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t51 @t144))) % 0.51/0.74 (step @p180 :rule symm :premises (@p179)) % 0.51/0.74 (step @p181 :rule eq_resolve :premises (@p178 @p180)) % 0.51/0.74 (step @p182 :rule cong :premises (@p181) :args (@t53)) % 0.51/0.74 (step @p183 :rule cong :premises (@p182) :args (@t55)) % 0.51/0.74 (step @p184 :rule trans :premises (@p34 @p183)) % 0.51/0.74 (step @p185 :rule ho_cong :premises (@p184 @p176)) % 0.51/0.74 (step @p186 :rule refl :args (@t122)) % 0.51/0.74 (step @p187 :rule refl :args (@t33)) % 0.51/0.74 (step @p188 :rule cong :premises (@p187 @p186) :args ((= @t33 @t122))) % 0.51/0.74 (step @p189 :rule symm :premises (@p188)) % 0.51/0.74 (step @p190 :rule eq_resolve :premises (@p187 @p189)) % 0.51/0.74 (step @p191 :rule cong :premises (@p190) :args (@t104)) % 0.51/0.74 (step @p192 :rule cong :premises (@p191) :args (@t106)) % 0.51/0.74 (step @p193 :rule trans :premises (@p51 @p192)) % 0.51/0.74 (step @p194 :rule ho_cong :premises (@p193 @p185)) % 0.51/0.74 (step @p195 :rule trans :premises (@p194 @p128)) % 0.51/0.74 (step @p196 :rule eq_resolve :premises (@p2 @p195)) % 0.51/0.74 (step @p197 :rule beta-reduce :args ((= @t175 @t173))) % 0.51/0.74 (step @p198 :rule cong :premises (@p197) :args (@t176)) % 0.51/0.74 (step @p199 :rule beta-reduce :args ((= (_ @t123 @t174) @t176))) % 0.51/0.74 (step @p200 :rule trans :premises (@p199 @p198)) % 0.51/0.74 (step @p201 :rule beta-reduce :args ((= @t178 @t137))) % 0.51/0.74 (step @p202 :rule cong :premises (@p201) :args (@t179)) % 0.51/0.74 (step @p203 :rule cong :premises (@p202) :args (@t180)) % 0.51/0.74 (step @p204 :rule cong :premises (@p203) :args (@t181)) % 0.51/0.74 (step @p205 :rule cong :premises (@p204) :args (@t182)) % 0.51/0.74 (step @p206 :rule beta-reduce :args ((= (_ @t184 @t177) @t182))) % 0.51/0.74 (step @p207 :rule trans :premises (@p206 @p205)) % 0.51/0.74 (step @p208 :rule ho_cong :premises (@p116 @p90)) % 0.51/0.74 (step @p209 :rule trans :premises (@p208 @p91)) % 0.51/0.74 (step @p210 :rule cong :premises (@p209) :args (@t185)) % 0.51/0.74 (step @p211 :rule refl :args (@t184)) % 0.51/0.74 (step @p212 :rule ho_cong :premises (@p211 @p210)) % 0.51/0.74 (step @p213 :rule trans :premises (@p212 @p207)) % 0.51/0.74 (step @p214 :rule ho_cong :premises (@p126 @p213)) % 0.51/0.74 (step @p215 :rule trans :premises (@p214 @p200)) % 0.51/0.74 (step @p216 :rule cong :premises (@p215) :args ((not (_ @t123 (_ @t184 @t185))))) % 0.51/0.74 (step @p217 :rule ho_cong :premises (@p146 @p90)) % 0.51/0.74 (step @p218 :rule cong :premises (@p217) :args (@t24)) % 0.51/0.74 (step @p219 :rule beta-reduce :args ((= (_ (lambda @t64 (not @t186)) @t1) @t183))) % 0.51/0.74 (step @p220 :rule beta-reduce :args ((= @t188 @t186))) % 0.51/0.74 (step @p221 :rule cong :premises (@p220) :args (@t189)) % 0.51/0.74 (step @p222 :rule cong :premises (@p221) :args (@t190)) % 0.51/0.74 (step @p223 :rule beta-reduce :args ((= (_ @t36 @t187) @t190))) % 0.51/0.74 (step @p224 :rule trans :premises (@p223 @p222)) % 0.51/0.74 (step @p225 :rule cong :premises (@p181) :args (@t191)) % 0.51/0.74 (step @p226 :rule cong :premises (@p225) :args ((forall @t52 @t191))) % 0.51/0.74 (step @p227 :rule beta-reduce :args ((= @t194 @t191))) % 0.51/0.74 (step @p228 :rule cong :premises (@p227) :args (@t195)) % 0.51/0.74 (step @p229 :rule trans :premises (@p228 @p226)) % 0.51/0.74 (step @p230 :rule cong :premises (@p229) :args (@t196)) % 0.51/0.74 (step @p231 :rule beta-reduce :args ((= (_ @t145 @t193) @t196))) % 0.51/0.74 (step @p232 :rule trans :premises (@p231 @p230)) % 0.51/0.74 (step @p233 :rule beta-reduce :args ((= (_ @t197 @t1) @t192))) % 0.51/0.74 (step @p234 :rule beta-reduce :args ((= @t198 @t197))) % 0.51/0.74 (step @p235 :rule ho_cong :premises (@p234 @p90)) % 0.51/0.74 (step @p236 :rule trans :premises (@p235 @p233)) % 0.51/0.74 (step @p237 :rule cong :premises (@p236) :args ((lambda @t7 (_ @t198 @t1)))) % 0.51/0.74 (step @p238 :rule ho_cong :premises (@p123 @p237)) % 0.51/0.74 (step @p239 :rule trans :premises (@p238 @p232)) % 0.51/0.74 (step @p240 :rule refl :args (@t36)) % 0.51/0.74 (step @p241 :rule ho_cong :premises (@p240 @p239)) % 0.51/0.74 (step @p242 :rule trans :premises (@p241 @p224)) % 0.51/0.74 (step @p243 :rule ho_cong :premises (@p242 @p90)) % 0.51/0.74 (step @p244 :rule trans :premises (@p243 @p219)) % 0.51/0.74 (step @p245 :rule refl :args (@t50)) % 0.51/0.74 (step @p246 :rule ho_cong :premises (@p27 @p245)) % 0.51/0.74 (step @p247 :rule ho_cong :premises (@p246 @p90)) % 0.51/0.74 (step @p248 :rule cong :premises (@p247) :args (@t60)) % 0.51/0.74 (step @p249 :rule ho_cong :premises (@p184 @p248)) % 0.51/0.74 (step @p250 :rule ho_cong :premises (@p27 @p249)) % 0.51/0.74 (step @p251 :rule ho_cong :premises (@p250 @p90)) % 0.51/0.74 (step @p252 :rule trans :premises (@p251 @p244)) % 0.51/0.74 (step @p253 :rule cong :premises (@p252) :args (@t62)) % 0.51/0.74 (step @p254 :rule trans :premises (@p36 @p253)) % 0.51/0.74 (step @p255 :rule ho_cong :premises (@p254 @p218)) % 0.51/0.74 (step @p256 :rule ho_cong :premises (@p193 @p255)) % 0.51/0.74 (step @p257 :rule cong :premises (@p256) :args (@t25)) % 0.51/0.74 (step @p258 :rule trans :premises (@p257 @p216)) % 0.51/0.74 (step @p259 :rule eq_resolve :premises (@p23 @p258)) % 0.51/0.74 (step @p260 :rule refl :args (@t202)) % 0.51/0.74 (step @p261 :rule bool-double-not-elim :args (@t199)) % 0.51/0.74 (step @p262 :rule nary_cong :premises (@p261 @p260) :args ((or (not @t203) @t202))) % 0.51/0.74 (step @p263 :rule bool-double-not-elim :args (@t202)) % 0.51/0.74 (step @p264 :rule refl :args (@t203)) % 0.51/0.74 (step @p265 :rule cong :premises (@p264 @p263) :args ((=> @t203 @t204))) % 0.51/0.74 (assume-push @p310 @t203) % 0.51/0.74 (step @p267 :rule skolemize :premises (@p259)) % 0.51/0.74 (step-pop @p311 :rule scope :premises (@p267)) % 0.51/0.74 (step @p268 :rule process_scope :premises (@p311) :args (@t204)) % 0.51/0.74 (step @p270 :rule eq_resolve :premises (@p268 @p265)) % 0.51/0.74 (step @p271 :rule implies_elim :premises (@p270)) % 0.51/0.74 (step @p272 :rule eq_resolve :premises (@p271 @p262)) % 0.51/0.74 (step @p273 :rule chain_m_resolution :premises (@p272 @p259) :args (@t202 @t205 (@list @t199))) % 0.51/0.74 (step @p274 :rule instantiate :premises (@p273) :args ((@list tptp.john))) % 0.51/0.74 (step @p275 :rule skolemize :premises (@p274)) % 0.51/0.74 (step @p276 :rule cnf_or_neg :args (@t210 1)) % 0.51/0.74 (step @p277 :rule chain_m_resolution :premises (@p276 @p275) :args ((not @t207) @t205 @t211)) % 0.51/0.74 (step @p278 :rule bool-double-not-elim :args (@t208)) % 0.51/0.74 (step @p279 :rule refl :args (@t210)) % 0.51/0.74 (step @p280 :rule nary_cong :premises (@p279 @p278) :args ((or @t210 (not @t209)))) % 0.51/0.74 (step @p281 :rule cnf_or_neg :args (@t210 0)) % 0.51/0.74 (step @p282 :rule eq_resolve :premises (@p281 @p280)) % 0.51/0.74 (step @p283 :rule reordering :premises (@p282) :args ((or @t208 @t210))) % 0.51/0.74 (step @p284 :rule chain_m_resolution :premises (@p283 @p275) :args (@t208 @t205 @t211)) % 0.51/0.74 (step @p285 :rule refl :args (@t212)) % 0.51/0.74 (step @p286 :rule refl :args (@t213)) % 0.51/0.74 (step @p287 :rule cong :premises (@p286 @p285) :args ((= @t213 @t212))) % 0.51/0.74 (step @p288 :rule symm :premises (@p287)) % 0.51/0.74 (step @p289 :rule eq_resolve :premises (@p286 @p288)) % 0.51/0.74 (step @p290 :rule cong :premises (@p289) :args ((forall @t64 @t213))) % 0.51/0.74 (step @p291 :rule refl :args (@t214)) % 0.51/0.74 (step @p292 :rule cong :premises (@p291) :args (@t215)) % 0.51/0.74 (step @p293 :rule trans :premises (@p292 @p290)) % 0.51/0.74 (step @p294 :rule beta-reduce :args ((= (_ @t123 @t23) @t215))) % 0.51/0.74 (step @p295 :rule trans :premises (@p294 @p293)) % 0.51/0.74 (step @p296 :rule refl :args (@t23)) % 0.51/0.74 (step @p297 :rule ho_cong :premises (@p193 @p296)) % 0.51/0.74 (step @p298 :rule trans :premises (@p297 @p295)) % 0.51/0.74 (step @p299 :rule eq_resolve :premises (@p19 @p298)) % 0.51/0.74 (step @p300 :rule instantiate :premises (@p299) :args ((@list @t200))) % 0.51/0.74 (step @p301 :rule cnf_or_pos :args (@t218)) % 0.51/0.74 (step @p302 :rule reordering :premises (@p301) :args ((or @t217 @t209 @t207 @t219))) % 0.51/0.74 (step @p303 :rule chain_m_resolution :premises (@p302 @p300 @p284 @p277) :args (@t219 (@list false false true) (@list @t216 @t208 @t207))) % 0.51/0.74 (assume-push @p312 @t116) % 0.51/0.74 (step @p305 :rule instantiate :premises (@p196) :args ((@list @t200 tptp.john @t206))) % 0.51/0.74 (step-pop @p313 :rule scope :premises (@p305)) % 0.51/0.74 (step @p306 :rule process_scope :premises (@p313) :args (@t218)) % 0.51/0.74 (step @p308 :rule implies_elim :premises (@p306)) % 0.51/0.74 (step @p309 false :rule chain_m_resolution :premises (@p308 @p303 @p196) :args (false (@list true false) (@list @t218 @t116))) % 0.51/0.74 ) % 0.51/0.74 % SZS output end Proof % 0.51/0.74 % cvc5 exiting %------------------------------------------------------------------------------