TSTP Solution File: NUM016-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM016-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n013.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 May 29 17:32:36 EDT 2024
% Result : Unsatisfiable 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM016-1 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue May 28 00:32:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.OaWIH1D45D/cvc5---1.0.5_27294.smt2
% 0.20/0.53 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.OaWIH1D45D/cvc5---1.0.5_27294.smt2
% 0.20/0.53 (assume a0 (forall ((X $$unsorted)) (not (tptp.less X X))))
% 0.20/0.53 (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.less X Y)) (not (tptp.less Y X)))))
% 0.20/0.53 (assume a2 (forall ((X $$unsorted)) (tptp.divides X X)))
% 0.20/0.53 (assume a3 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.divides Y Z)) (tptp.divides X Z))))
% 0.20/0.53 (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))))
% 0.20/0.53 (assume a5 (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))))
% 0.20/0.53 (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))))
% 0.20/0.53 (assume a7 (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))))
% 0.20/0.53 (assume a8 (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))))
% 0.20/0.53 (assume a9 (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.less (tptp.prime_divisor X) X))))
% 0.20/0.53 (assume a10 (tptp.prime tptp.a))
% 0.20/0.53 (assume a11 (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))))
% 0.20/0.53 (step t1 (cl (not (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) :rule or_pos)
% 0.20/0.53 (step t2 (cl (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule reordering :premises (t1))
% 0.20/0.53 (step t3 (cl (not (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) :rule or_pos)
% 0.20/0.53 (step t4 (cl (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))) (not (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule reordering :premises (t3))
% 0.20/0.53 (step t5 (cl (not (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) :rule or_pos)
% 0.20/0.53 (step t6 (cl (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)) (not (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))))) :rule reordering :premises (t5))
% 0.20/0.53 (step t7 (cl (not (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))) :rule or_pos)
% 0.20/0.53 (step t8 (cl (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)) (not (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule reordering :premises (t7))
% 0.20/0.53 (step t9 (cl (=> (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t10)
% 0.20/0.53 (assume t10.a0 (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))))
% 0.20/0.53 (step t10.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X)))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 0.20/0.53 (step t10.t2 (cl (not (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X)))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) :rule or :premises (t10.t1))
% 0.20/0.53 (step t10.t3 (cl (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) :rule resolution :premises (t10.t2 t10.a0))
% 0.20/0.53 (step t10 (cl (not (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X)))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) :rule subproof :discharge (t10.a0))
% 0.20/0.53 (step t11 (cl (=> (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) :rule resolution :premises (t9 t10))
% 0.20/0.53 (step t12 (cl (=> (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a)))) :rule implies_neg2)
% 0.20/0.53 (step t13 (cl (=> (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (=> (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t11 t12))
% 0.20/0.53 (step t14 (cl (=> (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a)))) :rule contraction :premises (t13))
% 0.20/0.53 (step t15 (cl (not (forall ((X $$unsorted)) (tptp.less X (tptp.factorial_plus_one X)))) (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) :rule implies :premises (t14))
% 0.20/0.53 (step t16 (cl (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) :rule resolution :premises (t15 a5))
% 0.20/0.53 (step t17 (cl (=> (forall ((X $$unsorted)) (not (tptp.less X X))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (forall ((X $$unsorted)) (not (tptp.less X X)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t18)
% 0.20/0.53 (assume t18.a0 (forall ((X $$unsorted)) (not (tptp.less X X))))
% 0.20/0.53 (step t18.t1 (cl (or (not (forall ((X $$unsorted)) (not (tptp.less X X)))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule forall_inst :args ((:= X (tptp.factorial_plus_one tptp.a))))
% 0.20/0.53 (step t18.t2 (cl (not (forall ((X $$unsorted)) (not (tptp.less X X)))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule or :premises (t18.t1))
% 0.20/0.53 (step t18.t3 (cl (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t18.t2 t18.a0))
% 0.20/0.53 (step t18 (cl (not (forall ((X $$unsorted)) (not (tptp.less X X)))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule subproof :discharge (t18.a0))
% 0.20/0.53 (step t19 (cl (=> (forall ((X $$unsorted)) (not (tptp.less X X))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t17 t18))
% 0.20/0.53 (step t20 (cl (=> (forall ((X $$unsorted)) (not (tptp.less X X))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (not (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule implies_neg2)
% 0.20/0.53 (step t21 (cl (=> (forall ((X $$unsorted)) (not (tptp.less X X))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (=> (forall ((X $$unsorted)) (not (tptp.less X X))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t19 t20))
% 0.20/0.53 (step t22 (cl (=> (forall ((X $$unsorted)) (not (tptp.less X X))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule contraction :premises (t21))
% 0.20/0.53 (step t23 (cl (not (forall ((X $$unsorted)) (not (tptp.less X X)))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule implies :premises (t22))
% 0.20/0.53 (step t24 (cl (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t23 a0))
% 0.20/0.53 (step t25 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t26)
% 0.20/0.53 (assume t26.a0 (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))))
% 0.20/0.53 (step t26.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule forall_inst :args ((:= X (tptp.factorial_plus_one tptp.a))))
% 0.20/0.53 (step t26.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule or :premises (t26.t1))
% 0.20/0.53 (step t26.t3 (cl (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t26.t2 t26.a0))
% 0.20/0.53 (step t26 (cl (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule subproof :discharge (t26.a0))
% 0.20/0.53 (step t27 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t25 t26))
% 0.20/0.53 (step t28 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (not (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule implies_neg2)
% 0.20/0.53 (step t29 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t27 t28))
% 0.20/0.53 (step t30 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a))))) :rule contraction :premises (t29))
% 0.20/0.53 (step t31 (cl (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule implies :premises (t30))
% 0.20/0.53 (step t32 (cl (or (not (tptp.prime (tptp.factorial_plus_one tptp.a))) (not (tptp.less tptp.a (tptp.factorial_plus_one tptp.a))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t31 a11))
% 0.20/0.53 (step t33 (cl (not (tptp.prime (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t8 t16 t24 t32))
% 0.20/0.53 (step t34 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t35)
% 0.20/0.53 (assume t35.a0 (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))))
% 0.20/0.53 (step t35.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))))) :rule forall_inst :args ((:= X (tptp.factorial_plus_one tptp.a))))
% 0.20/0.53 (step t35.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) :rule or :premises (t35.t1))
% 0.20/0.53 (step t35.t3 (cl (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t35.t2 t35.a0))
% 0.20/0.53 (step t35 (cl (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) :rule subproof :discharge (t35.a0))
% 0.20/0.53 (step t36 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t34 t35))
% 0.20/0.53 (step t37 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) (not (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))))) :rule implies_neg2)
% 0.20/0.53 (step t38 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t36 t37))
% 0.20/0.53 (step t39 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))))) :rule contraction :premises (t38))
% 0.20/0.53 (step t40 (cl (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.divides (tptp.prime_divisor X) X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) :rule implies :premises (t39))
% 0.20/0.53 (step t41 (cl (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t40 a7))
% 0.20/0.53 (step t42 (cl (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) :rule resolution :premises (t6 t33 t41))
% 0.20/0.53 (step t43 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t44)
% 0.20/0.53 (assume t44.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))))
% 0.20/0.53 (step t44.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule forall_inst :args ((:= X (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))) (:= Y tptp.a)))
% 0.20/0.53 (step t44.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule or :premises (t44.t1))
% 0.20/0.53 (step t44.t3 (cl (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t44.t2 t44.a0))
% 0.20/0.53 (step t44 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule subproof :discharge (t44.a0))
% 0.20/0.53 (step t45 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t43 t44))
% 0.20/0.53 (step t46 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (not (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule implies_neg2)
% 0.20/0.53 (step t47 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule resolution :premises (t45 t46))
% 0.20/0.53 (step t48 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule contraction :premises (t47))
% 0.20/0.53 (step t49 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X (tptp.factorial_plus_one Y))) (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule implies :premises (t48))
% 0.20/0.53 (step t50 (cl (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t49 a6))
% 0.20/0.53 (step t51 (cl (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t4 t42 t50))
% 0.20/0.53 (step t52 (cl (not (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule or_pos)
% 0.20/0.53 (step t53 (cl (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))))) :rule reordering :premises (t52))
% 0.20/0.53 (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X))))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t55)
% 0.20/0.53 (assume t55.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))))
% 0.20/0.53 (step t55.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X))))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))))) :rule forall_inst :args ((:= X (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))) (:= Y (tptp.factorial_plus_one tptp.a))))
% 0.20/0.53 (step t55.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X))))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule or :premises (t55.t1))
% 0.20/0.53 (step t55.t3 (cl (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule resolution :premises (t55.t2 t55.a0))
% 0.20/0.53 (step t55 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X))))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule subproof :discharge (t55.a0))
% 0.20/0.53 (step t56 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule resolution :premises (t54 t55))
% 0.20/0.53 (step t57 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) (not (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))))) :rule implies_neg2)
% 0.20/0.53 (step t58 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))))) :rule resolution :premises (t56 t57))
% 0.20/0.53 (step t59 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X)))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))))) :rule contraction :premises (t58))
% 0.20/0.53 (step t60 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.divides X Y)) (not (tptp.less Y X))))) (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule implies :premises (t59))
% 0.20/0.53 (step t61 (cl (or (not (tptp.divides (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)) (tptp.factorial_plus_one tptp.a))) (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule resolution :premises (t60 a4))
% 0.20/0.53 (step t62 (cl (not (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t53 t42 t61))
% 0.20/0.53 (step t63 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t64)
% 0.20/0.53 (assume t64.a0 (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))))
% 0.20/0.53 (step t64.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule forall_inst :args ((:= X (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))
% 0.20/0.53 (step t64.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule or :premises (t64.t1))
% 0.20/0.53 (step t64.t3 (cl (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t64.t2 t64.a0))
% 0.20/0.53 (step t64 (cl (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule subproof :discharge (t64.a0))
% 0.20/0.53 (step t65 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t63 t64))
% 0.20/0.53 (step t66 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (not (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule implies_neg2)
% 0.20/0.53 (step t67 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule resolution :premises (t65 t66))
% 0.20/0.53 (step t68 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule contraction :premises (t67))
% 0.20/0.53 (step t69 (cl (not (forall ((X $$unsorted)) (or (not (tptp.prime X)) (not (tptp.less tptp.a X)) (tptp.less (tptp.factorial_plus_one tptp.a) X)))) (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule implies :premises (t68))
% 0.20/0.53 (step t70 (cl (or (not (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (not (tptp.less tptp.a (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) (tptp.less (tptp.factorial_plus_one tptp.a) (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t69 a11))
% 0.20/0.53 (step t71 (cl (not (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) :rule or_pos)
% 0.20/0.53 (step t72 (cl (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))) (not (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule reordering :premises (t71))
% 0.20/0.53 (step t73 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X))))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t74)
% 0.20/0.53 (assume t74.a0 (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))))
% 0.20/0.53 (step t74.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X))))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule forall_inst :args ((:= X (tptp.factorial_plus_one tptp.a))))
% 0.20/0.53 (step t74.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X))))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule or :premises (t74.t1))
% 0.20/0.53 (step t74.t3 (cl (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t74.t2 t74.a0))
% 0.20/0.53 (step t74 (cl (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X))))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule subproof :discharge (t74.a0))
% 0.20/0.53 (step t75 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t73 t74))
% 0.20/0.53 (step t76 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (not (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule implies_neg2)
% 0.20/0.53 (step t77 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule resolution :premises (t75 t76))
% 0.20/0.53 (step t78 (cl (=> (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X)))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))))) :rule contraction :premises (t77))
% 0.20/0.53 (step t79 (cl (not (forall ((X $$unsorted)) (or (tptp.prime X) (tptp.prime (tptp.prime_divisor X))))) (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule implies :premises (t78))
% 0.20/0.53 (step t80 (cl (or (tptp.prime (tptp.factorial_plus_one tptp.a)) (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a))))) :rule resolution :premises (t79 a8))
% 0.20/0.53 (step t81 (cl (tptp.prime (tptp.prime_divisor (tptp.factorial_plus_one tptp.a)))) :rule resolution :premises (t72 t33 t80))
% 0.20/0.53 (step t82 (cl) :rule resolution :premises (t2 t51 t62 t70 t81))
% 0.20/0.53
% 0.20/0.53 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.OaWIH1D45D/cvc5---1.0.5_27294.smt2
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.37/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------