TSTP Solution File: SYN067-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYN067-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 : Fri May 19 12:27:11 EDT 2023
% Result : Unsatisfiable 13.00s 3.22s
% Output : Refutation 13.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 69
% Syntax : Number of formulae : 187 ( 3 unt; 14 typ; 0 def)
% Number of atoms : 891 ( 69 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 2553 ( 473 ~; 666 |; 0 &;1414 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 357 ( 0 ^; 357 !; 0 ?; 357 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_r_type,type,
big_r: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(big_p_type,type,
big_p: $i > $o ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(a_type,type,
a: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(52,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk10 @ C )
| ~ ( big_r @ sk7 @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_52) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk10 @ C )
| ~ ( big_r @ sk7 @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk10 @ C )
| ~ ( big_r @ sk7 @ D ) ),
inference(cnf,[status(esa)],[67]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk7 @ D )
| ( ( big_r @ sk10 @ C )
!= ( big_r @ C @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[117]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ sk10 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk10 @ sk10 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk7 @ B ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( sk10 )),bind(B,$thf( B )),bind(C,$thf( sk10 ))]]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ sk10 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk10 @ sk10 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk7 @ B ) ),
inference(simp,[status(thm)],[194]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ sk10 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk10 @ sk10 )
| ~ ( big_r @ sk7 @ B )
| ( ( big_r @ B @ A )
!= ( big_r @ sk10 @ sk10 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[198]) ).
thf(215,plain,
( ~ ( big_p @ sk10 )
| ~ ( big_p @ sk10 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk10 @ sk10 )
| ~ ( big_r @ sk7 @ sk10 ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( sk10 )),bind(B,$thf( sk10 ))]]) ).
thf(217,plain,
( ~ ( big_p @ sk10 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk10 @ sk10 )
| ~ ( big_r @ sk7 @ sk10 ) ),
inference(simp,[status(thm)],[215]) ).
thf(37,negated_conjecture,
big_p @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_37) ).
thf(65,plain,
big_p @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(38,negated_conjecture,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_38) ).
thf(75,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(154,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
inference(cnf,[status(esa)],[75]) ).
thf(166,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk7 )
| ( ( big_p @ sk9 )
!= ( big_p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[65,154]) ).
thf(169,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk7 )
| ( sk9 != a ) ),
inference(simp,[status(thm)],[166]) ).
thf(165,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk9 )
| ( ( big_p @ sk7 )
!= ( big_p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[65,154]) ).
thf(168,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk9 )
| ( sk7 != a ) ),
inference(simp,[status(thm)],[165]) ).
thf(172,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ( sk7 != a )
| ( ( big_p @ sk9 )
!= ( big_p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[65,168]) ).
thf(173,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ( sk7 != a )
| ( sk9 != a ) ),
inference(simp,[status(thm)],[172]) ).
thf(20,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_20) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(40,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk10 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_40) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( big_p @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk10 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(54,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk7 @ D )
| ~ ( big_r @ sk9 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_54) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk7 @ D )
| ~ ( big_r @ sk9 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(36,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_p @ ( sk3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_36) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_p @ ( sk3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_p @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( ( big_p @ ( sk3 @ A ) )
!= ( big_p @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[139]) ).
thf(261,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( big_p @ ( sk1 @ ( sk3 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C ))]]) ).
thf(272,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( big_p @ ( sk1 @ ( sk3 @ A ) ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(384,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
!= ( big_p @ ( sk3 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[272]) ).
thf(385,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
!= ( big_p @ ( sk3 @ A ) ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(5,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_5) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk5 @ B ) )
| ( big_r @ A @ ( sk2 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_15) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk5 @ B ) )
| ( big_r @ A @ ( sk2 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_30) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(35,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ A @ ( sk4 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_35) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ A @ ( sk4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(10,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_10) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ B @ ( sk6 @ B ) )
| ( big_r @ A @ ( sk2 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_13) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ B @ ( sk6 @ B ) )
| ( big_r @ A @ ( sk2 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_22) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(386,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(754,plain,
! [A: $i] :
( ( big_p @ A )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk3 @ A ) )
| ( ( big_p @ ( sk3 @ A ) )
!= ( big_p @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[386]) ).
thf(766,plain,
! [A: $i] :
( ( big_p @ A )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk3 @ A ) )
| ( ( sk3 @ A )
!= A ) ),
inference(simp,[status(thm)],[754]) ).
thf(8,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk5 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_8) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk5 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk10 @ C )
| ~ ( big_r @ sk9 @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_49) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk10 @ C )
| ~ ( big_r @ sk9 @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(28,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_28) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(300,plain,
( ( big_p @ sk11 )
| ( sk7 != a )
| ( sk9 != a )
| ( ( big_p @ sk8 )
!= ( big_p @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[173]) ).
thf(307,plain,
( ( big_p @ sk11 )
| ( sk7 != a )
| ( sk9 != a )
| ( sk8 != sk11 ) ),
inference(simp,[status(thm)],[300]) ).
thf(44,negated_conjecture,
( ( big_p @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_44) ).
thf(85,plain,
( ( big_p @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_26) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ A @ ( sk2 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_2) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ A @ ( sk2 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,negated_conjecture,
! [B: $i,A: $i] :
( ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk10 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_46) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk10 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk3 @ A ) )
| ( ( big_p @ ( sk1 @ B ) )
!= ( big_p @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[139]) ).
thf(264,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( big_p @ ( sk3 @ ( sk1 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( sk1 @ C )),bind(B,$thf( C ))]]) ).
thf(273,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( big_p @ ( sk3 @ ( sk1 @ A ) ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(421,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
!= ( big_p @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[273]) ).
thf(424,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( ( sk3 @ ( sk1 @ A ) )
!= A ) ),
inference(simp,[status(thm)],[421]) ).
thf(3,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ A @ ( sk6 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_3) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ A @ ( sk6 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_16) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(47,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_47) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( big_p @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(53,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk7 @ D )
| ~ ( big_r @ sk9 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_53) ).
thf(77,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk7 @ D )
| ~ ( big_r @ sk9 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(50,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk7 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_50) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( big_p @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk7 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(33,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ A ) )
| ( big_p @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_33) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ A ) )
| ( big_p @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(489,plain,
( ~ ( big_p @ sk10 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk7 @ sk10 )
| ( ( big_r @ sk10 @ sk10 )
!= ( big_r @ sk7 @ sk10 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[217]) ).
thf(503,plain,
( ~ ( big_p @ sk10 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 )
| ( sk10 != sk10 ) ),
inference(simp,[status(thm)],[489]) ).
thf(508,plain,
( ~ ( big_p @ sk10 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 ) ),
inference(simp,[status(thm)],[503]) ).
thf(420,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
!= ( big_p @ ( sk1 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[273]) ).
thf(430,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
!= ( big_p @ ( sk1 @ A ) ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(24,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ B ) )
| ( big_p @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_24) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ B ) )
| ( big_p @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(423,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
!= ( big_p @ A ) ) ),
inference(simp,[status(thm)],[421]) ).
thf(509,plain,
( ~ ( big_p @ sk9 )
| ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 )
| ( ( big_p @ sk10 )
!= ( big_p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[65,508]) ).
thf(531,plain,
( ~ ( big_p @ sk9 )
| ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 )
| ( sk10 != a ) ),
inference(simp,[status(thm)],[509]) ).
thf(810,plain,
( ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 )
| ( sk10 != a )
| ( ( big_p @ sk9 )
!= ( big_p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[65,531]) ).
thf(826,plain,
( ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 )
| ( sk10 != a )
| ( sk9 != a ) ),
inference(simp,[status(thm)],[810]) ).
thf(6,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_r @ B @ ( sk6 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_6) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_r @ B @ ( sk6 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_29) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(27,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ B @ ( sk2 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_27) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ B @ ( sk2 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk10 @ B ) ),
inference(cnf,[status(esa)],[70]) ).
thf(17,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ B @ ( sk2 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_17) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ B @ ( sk2 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_9) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_31) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(55,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ A )
| ~ ( big_r @ E @ B )
| ~ ( big_r @ F @ C )
| ~ ( big_r @ sk10 @ D )
| ~ ( big_r @ sk7 @ F )
| ~ ( big_r @ sk9 @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_55) ).
thf(103,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ A )
| ~ ( big_r @ E @ B )
| ~ ( big_r @ F @ C )
| ~ ( big_r @ sk10 @ D )
| ~ ( big_r @ sk7 @ F )
| ~ ( big_r @ sk9 @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ A @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(581,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ A @ ( sk4 @ A ) )
| ( ( big_p @ ( sk1 @ B ) )
!= ( big_p @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[122]) ).
thf(601,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( big_r @ ( sk1 @ A ) @ ( sk4 @ ( sk1 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( sk1 @ C )),bind(B,$thf( C ))]]) ).
thf(609,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( big_r @ ( sk1 @ A ) @ ( sk4 @ ( sk1 @ A ) ) ) ),
inference(simp,[status(thm)],[601]) ).
thf(39,negated_conjecture,
( ( big_p @ sk8 )
| ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_39) ).
thf(91,plain,
( ( big_p @ sk8 )
| ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(25,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_25) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_19) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(383,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
!= ( big_p @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[272]) ).
thf(395,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= A ) ),
inference(simp,[status(thm)],[383]) ).
thf(457,plain,
! [A: $i] :
( ( big_p @ A )
| ( ( sk1 @ ( sk3 @ A ) )
!= A )
| ( ( big_p @ ( sk3 @ A ) )
!= ( big_p @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[395]) ).
thf(462,plain,
! [A: $i] :
( ( big_p @ A )
| ( ( sk1 @ ( sk3 @ A ) )
!= A )
| ( ( sk3 @ A )
!= A ) ),
inference(simp,[status(thm)],[457]) ).
thf(394,plain,
! [A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
!= ( big_p @ A ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(431,plain,
! [A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_p @ A )
| ( ( sk3 @ ( sk1 @ A ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(45,negated_conjecture,
( ( big_r @ sk10 @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_45) ).
thf(80,plain,
( ( big_r @ sk10 @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ sk7 )
| ~ ( big_p @ sk9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(167,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk7 )
| ( ( big_p @ sk9 )
!= ( big_p @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[154]) ).
thf(171,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ sk7 )
| ( sk9 != sk7 ) ),
inference(simp,[status(thm)],[167]) ).
thf(280,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ( sk9 != sk7 )
| ( ( big_p @ sk7 )
!= ( big_p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[65,171]) ).
thf(283,plain,
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ( sk9 != sk7 )
| ( sk7 != a ) ),
inference(simp,[status(thm)],[280]) ).
thf(642,plain,
( ( big_p @ sk11 )
| ( sk9 != sk7 )
| ( sk7 != a )
| ( ( big_p @ sk8 )
!= ( big_p @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[283]) ).
thf(653,plain,
( ( big_p @ sk11 )
| ( sk9 != sk7 )
| ( sk7 != a )
| ( sk8 != sk11 ) ),
inference(simp,[status(thm)],[642]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk5 @ B ) )
| ( big_r @ A @ ( sk2 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(cnf,[status(esa)],[110]) ).
thf(42,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ sk8 )
| ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_42) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( big_p @ sk8 )
| ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(18,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_18) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ A @ ( sk4 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ A @ ( sk4 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_21) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ A @ ( sk4 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ B @ ( sk6 @ B ) )
| ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_11) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ B @ ( sk6 @ B ) )
| ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ A @ ( sk2 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_12) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_r @ A @ ( sk2 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_23) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk3 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_1) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(510,plain,
( ~ ( big_p @ sk10 )
| ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 )
| ( ( big_p @ sk9 )
!= ( big_p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[65,508]) ).
thf(536,plain,
( ~ ( big_p @ sk10 )
| ~ ( big_r @ sk7 @ sk10 )
| ( sk10 != sk7 )
| ( sk9 != a ) ),
inference(simp,[status(thm)],[510]) ).
thf(32,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ A ) )
| ( big_r @ B @ ( sk6 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_32) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk1 @ A ) )
| ( big_r @ B @ ( sk6 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(51,negated_conjecture,
! [B: $i,A: $i] :
( ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk7 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_51) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( big_r @ sk10 @ sk11 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk9 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk7 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(41,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_41) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( big_p @ sk11 )
| ( big_p @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(48,negated_conjecture,
! [B: $i,A: $i] :
( ( big_r @ sk10 @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_48) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( big_r @ sk10 @ sk11 )
| ( big_r @ sk7 @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ B @ A )
| ~ ( big_r @ sk9 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(14,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk5 @ B ) )
| ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_14) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ ( sk5 @ B ) )
| ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ~ ( big_p @ C )
| ~ ( big_r @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ A @ ( sk6 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_4) ).
thf(62,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_r @ A @ ( sk6 @ A ) )
| ( big_r @ B @ ( sk2 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(34,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_34) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( big_p @ A )
| ( big_p @ B )
| ( big_p @ ( sk1 @ B ) )
| ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(43,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk10 @ C )
| ~ ( big_r @ sk9 @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_43) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ sk8 )
| ~ ( big_p @ A )
| ~ ( big_p @ B )
| ~ ( big_p @ sk7 )
| ~ ( big_r @ C @ A )
| ~ ( big_r @ D @ B )
| ~ ( big_r @ sk10 @ C )
| ~ ( big_r @ sk9 @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(7,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk5 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_7) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk5 @ A ) )
| ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ A @ C )
| ~ ( big_r @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ ( sk1 @ A ) )
| ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
| ~ ( big_p @ C )
| ~ ( big_p @ D )
| ~ ( big_r @ B @ C )
| ~ ( big_r @ A @ D ) ),
inference(cnf,[status(esa)],[56]) ).
thf(2804,plain,
$false,
inference(cvc4,[status(thm)],[217,169,173,67,69,101,88,385,56,110,125,93,57,78,106,84,766,61,89,74,307,85,102,60,117,70,424,92,65,97,109,77,96,73,105,508,430,64,423,826,59,71,86,113,81,76,98,103,609,91,66,198,108,462,394,431,80,653,531,112,63,95,154,72,386,99,87,104,171,139,75,58,272,536,82,168,273,107,79,94,283,395,68,62,122,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN067-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 19:26:10 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.87/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.00 % [INFO] Parsing done (147ms).
% 1.20/1.01 % [INFO] Running in sequential loop mode.
% 1.88/1.21 % [INFO] eprover registered as external prover.
% 1.88/1.22 % [INFO] cvc4 registered as external prover.
% 1.88/1.22 % [INFO] Scanning for conjecture ...
% 2.24/1.35 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.43/1.44 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.43/1.44 % [INFO] Problem is propositional (TPTP CNF).
% 2.43/1.44 % [INFO] Type checking passed.
% 2.43/1.45 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 13.00/3.21 % External prover 'cvc4' found a proof!
% 13.00/3.22 % [INFO] Killing All external provers ...
% 13.00/3.22 % Time passed: 2687ms (effective reasoning time: 2206ms)
% 13.00/3.22 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.00/3.22 % Axioms used in derivation (0):
% 13.00/3.22 % No. of inferences in proof: 173
% 13.00/3.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2687 ms resp. 2206 ms w/o parsing
% 13.00/3.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.00/3.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------