TSTP Solution File: PLA050_1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : PLA050_1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% 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 : Thu Aug 31 12:59:45 EDT 2023

% Result   : Theorem 60.42s 60.67s
% Output   : Proof 60.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : PLA050_1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n012.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   : Sun Aug 27 06:07:55 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_ARI
% 60.42/60.67  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.cNOCJC8Th3/cvc5---1.0.5_18997.p...
% 60.42/60.67  ------- get file name : TPTP file name is PLA050_1
% 60.42/60.67  ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18997.smt2...
% 60.42/60.67  --- Run --finite-model-find --decision=internal at 15...
% 60.42/60.67  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 60.42/60.67  --- Run --no-e-matching --full-saturate-quant at 15...
% 60.42/60.67  --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 60.42/60.67  % SZS status Theorem for PLA050_1
% 60.42/60.67  % SZS output start Proof for PLA050_1
% 60.42/60.67  (
% 60.42/60.67  (let ((_let_1 (= (tptp.mylk 0) 1))) (let ((_let_2 (forall ((D Real) (T Int) (C Int)) (= (tptp.mysump D T C 0) 0.0)))) (let ((_let_3 (forall ((D Real) (T Int) (C Int)) (=> (<= 1 C) (= (* (to_real T) (tptp.imp D T C)) (+ (* D (to_real (tptp.lk (- C 1)))) (tptp.mysump D T C (- C 2)))))))) (let ((_let_4 (tptp.lk 1))) (let ((_let_5 (tptp.lk 0))) (let ((_let_6 (forall ((K Int)) (=> (and (<= 1 K) (<= K tptp.problen)) (<= (tptp.lk (- K 1)) (tptp.lk K)))))) (let ((_let_7 (= _let_5 1))) (let ((_let_8 (not (forall ((S Real) (C Int) (Problen Int) (Probsize Int)) (=> (and (<= 2 Problen) (= tptp.problen Problen) (<= (* Problen Problen) Probsize) (= tptp.probsize Probsize) (<= (* C 2) tptp.problen) (<= (to_real tptp.probsize) (tptp.recexp S tptp.probsize C)) (<= (/ 9 10) S) (<= S 10.0)) (<= S 1.0)))))) (let ((_let_9 (+ _let_5 (* (- 1) _let_4)))) (let ((_let_10 (>= _let_9 1))) (let ((_let_11 (tptp.mysump (/ (- 1) 3) 0 2 0))) (let ((_let_12 (= _let_11 0.0))) (let ((_let_13 (= _let_11 (* (/ 1 3) _let_4)))) (let ((_let_14 (ASSUME :args (_let_7)))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_16 (NOT_NOT_ELIM (NOT_OR_ELIM _let_15 :args (1))))) (let ((_let_17 (not _let_10))) (let ((_let_18 (>= tptp.problen 1))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17))) (let ((_let_21 (forall ((K Int)) (or (not (>= K 1)) (not (>= (+ tptp.problen (* (- 1) K)) 0)) (>= (+ (tptp.lk K) (* (- 1) (tptp.lk (+ (- 1) K)))) 0))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (>= tptp.problen 2))) (let ((_let_24 (or))) (let ((_let_25 (> tptp.problen 0))) (let ((_let_26 (ASSUME :args (_let_19)))) (let ((_let_27 ((<= tptp.problen 0)))) (let ((_let_28 (false))) (let ((_let_29 (ASSUME :args (_let_23)))) (let ((_let_30 (_let_2))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (forall ((D Real) (T Int) (C Int)) (or (not (>= C 1)) (= (tptp.mysump D T C (+ (- 2) C)) (+ (* (- 1) (* D (tptp.lk (+ (- 1) C)))) (* (tptp.imp D T C) T))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (< _let_9 1))) (let ((_let_35 (_let_34))) (let ((_let_36 (ASSUME :args (_let_12)))) (let ((_let_37 (ASSUME :args (_let_13)))) (let ((_let_38 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_14 _let_36 _let_37 _let_38) :args (_let_7 _let_17 _let_12 _let_13)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM _let_38 :args _let_35) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_35) (MACRO_SR_PRED_TRANSFORM _let_37 :args ((= (+ _let_11 (* (/ (- 1) 3) _let_4)) 0.0))) _let_36 _let_14 :args (1.0 (- 3.0) 3.0 (- 1.0))) :args _let_28) :args _let_35) :args (_let_10)) :args ((not _let_34)))) :args (_let_7 _let_12 _let_13 _let_17)) :args ((not (and _let_7 _let_17 _let_12 _let_13)) SB_LITERAL))) (CONG (REFL :args ((not _let_7))) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_10))) (REFL :args ((not _let_12))) (REFL :args ((not _let_13))) :args _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args ((/ (- 1) 3) 0 2 QUANTIFIERS_INST_E_MATCHING_VAR_GEN ((tptp.mysump D T C (+ (- 2) C))))) :args (_let_32)))) _let_33 :args (_let_13 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args ((/ (- 1) 3) 0 2 QUANTIFIERS_INST_CBQI_PROP)) :args _let_30)) _let_31 :args (_let_12 false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_17 (not _let_20)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_26 _let_29) :args (_let_23 _let_19)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_27) _let_29 :args (1.0 (- 1.0))) :args _let_28) :args _let_27) :args (_let_25)) (MACRO_SR_PRED_TRANSFORM (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_26 :args ((< tptp.problen 1)))) :args ((not _let_25)))) :args (_let_19 _let_23)) :args ((not (and _let_23 _let_19)) SB_LITERAL))) (CONG (REFL :args ((not _let_23))) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_24)) _let_16 :args (_let_18 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 :args (1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.lk K)))) :args (_let_21)))) _let_22 :args (_let_20 false _let_21)) :args (_let_17 false _let_18 false _let_20)) (AND_ELIM (AND_INTRO (NOT_OR_ELIM _let_15 :args (0)) _let_16 (NOT_NOT_ELIM (NOT_OR_ELIM _let_15 :args (2))) _let_14 (ASSUME :args (_let_1))) :args (3)) :args (false false _let_13 false _let_12 true _let_10 false _let_7)) :args (_let_8 _let_7 _let_6 (= (tptp.ns 0) (+ _let_5 _let_4)) (= (tptp.ns tptp.problen) (+ (tptp.lk (- tptp.problen 1)) (tptp.lk tptp.problen))) (forall ((K Int)) (=> (and (<= 1 K) (<= K (- tptp.problen 1))) (= (tptp.ns K) (+ (+ (tptp.lk (- K 1)) (tptp.lk K)) (tptp.lk (+ K 1)))))) (forall ((D Real) (T Int) (C Int)) (let ((_let_1 (tptp.ns C))) (= (* (tptp.dc D T C) (to_real (- T _let_1))) (- (to_real T) (* D (to_real _let_1)))))) (forall ((D Real) (T Int)) (= (tptp.imp D T 0) 0.0)) _let_3 _let_2 (forall ((D Real) (T Int) (C Int) (K Int)) (=> (<= 1 K) (= (tptp.mysump D T C K) (+ (* (tptp.dc D T C) (to_real (tptp.lk K))) (tptp.mysump D T C (- K 1)))))) (forall ((D Real) (T Int)) (= (tptp.recexp D T 0) 0.0)) (forall ((D Real) (T Int) (C Int)) (let ((_let_1 (- C 1))) (let ((_let_2 (to_real T))) (=> (<= 1 C) (= (* (tptp.imp D T C) (* _let_2 (tptp.recexp D T C))) (+ (+ _let_2 (* (* D (tptp.recexp D T _let_1)) (to_real (tptp.lk _let_1)))) (tptp.mysumr D T C (- C 2)))))))) _let_1 (forall ((K Int)) (=> (and (<= 1 K) (<= K tptp.problen)) (= (tptp.mylk K) (+ (tptp.lk K) (tptp.mylk (- K 1)))))) (<= (tptp.mylk tptp.problen) tptp.probsize) (forall ((D Real) (T Int) (C Int)) (= (tptp.mysumr D T C 0) 0.0)) (forall ((D Real) (T Int) (C Int) (K Int)) (=> (<= 1 K) (= (tptp.mysumr D T C K) (+ (* (tptp.dc D T C) (* (tptp.recexp D T K) (to_real (tptp.lk K)))) (tptp.mysumr D T C (- K 1)))))) true)))))))))))))))))))))))))))))))))))))))))
% 60.48/60.69  )
% 60.48/60.69  % SZS output end Proof for PLA050_1
% 60.48/60.69  % cvc5---1.0.5 exiting
% 60.48/60.69  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------