TSTP Solution File: SYN067-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYN067-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 12:27:10 EDT 2023
% Result : Unsatisfiable 5.19s 2.19s
% Output : Refutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 97
% Syntax : Number of formulae : 182 ( 2 unt; 13 typ; 0 def)
% Number of atoms : 996 ( 0 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 2998 ( 608 ~; 827 |; 0 &;1563 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 376 ( 0 ^; 376 !; 0 ?; 376 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_p_type,type,
big_p: $i > $o ).
thf(a_type,type,
a: $i ).
thf(f2_type,type,
f2: $i > $i ).
thf(f4_type,type,
f4: $i > $i ).
thf(big_r_type,type,
big_r: $i > $i > $o ).
thf(f3_type,type,
f3: $i > $i ).
thf(f6_type,type,
f6: $i > $i ).
thf(f5_type,type,
f5: $i > $i ).
thf(f1_type,type,
f1: $i > $i ).
thf(c3_type,type,
c3: $i ).
thf(c4_type,type,
c4: $i ).
thf(c2_type,type,
c2: $i ).
thf(c1_type,type,
c1: $i ).
thf(27,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ ( f3 @ C ) @ ( f4 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ ( f3 @ C ) @ ( f4 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(41,negated_conjecture,
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_41) ).
thf(118,plain,
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(44,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_44) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(73,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_73) ).
thf(119,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ ( f3 @ B ) @ ( f4 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ ( f3 @ B ) @ ( f4 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_46) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(65,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_65) ).
thf(88,plain,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ ( f3 @ B ) @ ( f4 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(115,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ ( f3 @ B ) @ ( f4 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ B @ ( f3 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ B @ ( f3 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_63) ).
thf(142,plain,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(55,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_55) ).
thf(153,plain,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(70,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_70) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(34,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_p @ ( f6 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_p @ ( f6 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(58,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_58) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(56,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_56) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(26,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ C @ ( f3 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ C @ ( f3 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(79,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_79) ).
thf(164,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_p @ ( f4 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_p @ ( f4 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(45,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_45) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(31,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_p @ ( f4 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_p @ ( f4 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_54) ).
thf(132,plain,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(53,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_53) ).
thf(116,plain,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(77,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_77) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(49,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_49) ).
thf(133,plain,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(13,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_p @ ( f4 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
thf(117,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_p @ ( f4 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(69,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_69) ).
thf(85,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(57,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_57) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(30,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ ( f5 @ D ) @ ( f6 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
thf(160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ ( f5 @ D ) @ ( f6 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,negated_conjecture,
( ( big_p @ a )
| ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_39) ).
thf(137,plain,
( ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(47,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_47) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(10,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_p @ ( f6 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_p @ ( f6 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_p @ ( f4 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_p @ ( f4 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(75,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_75) ).
thf(156,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(48,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_48) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(60,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_60) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(32,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ C @ ( f3 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_32) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ C @ ( f3 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,negated_conjecture,
( ( big_p @ a )
| ( big_p @ a )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
thf(96,plain,
big_p @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(81,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_81) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(59,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_59) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(61,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ( big_p @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_61) ).
thf(105,plain,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ( big_p @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(15,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ ( f3 @ B ) @ ( f4 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
thf(166,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ ( f3 @ B ) @ ( f4 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ C @ ( f5 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ C @ ( f5 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(51,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_51) ).
thf(161,plain,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(72,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_72) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(50,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).
thf(144,plain,
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(5,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ C @ ( f5 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ C @ ( f5 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ ( f5 @ D ) @ ( f6 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_36) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ ( f5 @ D ) @ ( f6 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(28,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_p @ ( f6 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_p @ ( f6 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(52,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_52) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_p @ c1 )
| ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(78,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_78) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(35,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ D @ ( f5 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_35) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ D @ ( f5 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(83,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_83) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(8,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ B @ ( f3 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(155,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ B @ ( f3 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ ( f5 @ C ) @ ( f6 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ ( f5 @ C ) @ ( f6 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(71,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_71) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(76,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_76) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(68,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_68) ).
thf(167,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(19,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_p @ ( f4 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_p @ ( f4 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ ( f3 @ C ) @ ( f4 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ ( f1 @ B ) @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ ( f3 @ C ) @ ( f4 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ C @ ( f5 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ C @ ( f5 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(67,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_67) ).
thf(145,plain,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(43,negated_conjecture,
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_43) ).
thf(150,plain,
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ( big_r @ c4 @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(24,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ ( f5 @ D ) @ ( f6 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ ( f5 @ D ) @ ( f6 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(23,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ D @ ( f5 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ D @ ( f5 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ ( f5 @ C ) @ ( f6 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ ( f5 @ C ) @ ( f6 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ B @ ( f3 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_r @ B @ ( f3 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(84,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ~ ( big_p @ E )
| ~ ( big_r @ c4 @ F )
| ~ ( big_r @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_84) ).
thf(87,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ~ ( big_p @ E )
| ~ ( big_r @ c4 @ F )
| ~ ( big_r @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(29,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ D @ ( f5 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_r @ B @ ( f1 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_r @ D @ ( f5 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(82,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_82) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(38,negated_conjecture,
( ( big_p @ a )
| ( big_p @ a )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_38) ).
thf(114,plain,
( ( big_p @ a )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(80,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_80) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ~ ( big_p @ c4 )
| ~ ( big_p @ C )
| ~ ( big_r @ c4 @ D )
| ~ ( big_r @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(40,negated_conjecture,
! [B: $i,A: $i] :
( ( big_p @ a )
| ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_40) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(62,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_62) ).
thf(168,plain,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(16,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_p @ ( f6 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ ( f1 @ A ) @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_p @ ( f6 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(74,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_74) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ A )
| ~ ( big_r @ c2 @ B )
| ~ ( big_r @ B @ A )
| ( big_p @ a )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(42,negated_conjecture,
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_42) ).
thf(94,plain,
( ( big_p @ a )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(22,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_p @ ( f6 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ~ ( big_p @ C )
| ~ ( big_r @ D @ C )
| ( big_p @ ( f6 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_p @ ( f4 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ( big_p @ B )
| ( big_p @ ( f4 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ ( f5 @ C ) @ ( f6 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_r @ A @ ( f1 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_r @ ( f5 @ C ) @ ( f6 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_p @ ( f6 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ( big_p @ A )
| ( big_p @ ( f2 @ A ) )
| ~ ( big_p @ a )
| ~ ( big_p @ B )
| ~ ( big_r @ C @ B )
| ( big_p @ ( f6 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_64) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ c4 @ B )
| ~ ( big_r @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(20,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ C @ ( f3 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ C @ ( f3 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(66,negated_conjecture,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).
thf(90,plain,
( ~ ( big_p @ c2 )
| ( big_r @ c2 @ c1 )
| ~ ( big_p @ c4 )
| ( big_p @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(21,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ ( f3 @ C ) @ ( f4 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( big_p @ a )
| ~ ( big_p @ A )
| ~ ( big_r @ B @ A )
| ( big_p @ ( f2 @ B ) )
| ~ ( big_p @ a )
| ( big_p @ C )
| ( big_r @ ( f3 @ C ) @ ( f4 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(323,plain,
$false,
inference(e,[status(thm)],[129,118,127,119,138,101,88,115,120,142,153,110,125,157,93,152,164,106,121,147,132,116,89,133,117,85,102,160,137,165,92,97,156,141,109,124,96,134,128,105,166,148,161,149,144,86,159,113,98,103,140,91,155,108,130,135,167,162,112,123,145,150,95,154,143,99,87,104,158,114,139,151,168,146,107,94,126,136,131,163,122,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SYN067-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu May 18 19:34:20 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.70/0.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.03/0.88 % [INFO] Parsing done (137ms).
% 1.03/0.89 % [INFO] Running in sequential loop mode.
% 1.55/1.08 % [INFO] eprover registered as external prover.
% 1.55/1.08 % [INFO] cvc4 registered as external prover.
% 1.63/1.08 % [INFO] Scanning for conjecture ...
% 1.99/1.22 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.10/1.31 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.31 % [INFO] Problem is propositional (TPTP CNF).
% 2.10/1.32 % [INFO] Type checking passed.
% 2.10/1.32 % [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 ...
% 5.19/2.18 % External prover 'e' found a proof!
% 5.19/2.18 % [INFO] Killing All external provers ...
% 5.19/2.18 % Time passed: 1743ms (effective reasoning time: 1291ms)
% 5.19/2.18 % 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)>
% 5.19/2.18 % Axioms used in derivation (0):
% 5.19/2.18 % No. of inferences in proof: 169
% 5.19/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1743 ms resp. 1291 ms w/o parsing
% 5.19/2.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.19/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------