TSTP Solution File: COL092-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL092-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Tue May 7 07:29:32 EDT 2024
% Result : Unsatisfiable 4.24s 2.08s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 82
% Syntax : Number of formulae : 138 ( 17 unt; 27 typ; 0 def)
% Number of atoms : 235 ( 46 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1108 ( 124 ~; 124 |; 0 &; 860 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 8 con; 0-3 aty)
% Number of variables : 264 ( 0 ^ 264 !; 0 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
thf(r_type,type,
r: $i ).
thf(comb_app_type,type,
comb_app: $i > $i > $i ).
thf(combK_type,type,
combK: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(p_type,type,
p: $i ).
thf(parcontract_type,type,
parcontract: $i ).
thf(comb_type,type,
comb: $i ).
thf(ap_parcontractE_c4_type,type,
ap_parcontractE_c4: $i > $i > $i > $o ).
thf(ap_parcontractE_sk2s_type,type,
ap_parcontractE_sk2s: $i > $i > $i > $i ).
thf(ap_contractE_c3_type,type,
ap_contractE_c3: $i > $i > $i > $o ).
thf(ap_contractE_sk2q_type,type,
ap_contractE_sk2q: $i > $i > $i > $i ).
thf(ap_contractE_c4_type,type,
ap_contractE_c4: $i > $i > $i > $o ).
thf(ap_contractE_sk3q_type,type,
ap_contractE_sk3q: $i > $i > $i > $i ).
thf(contract_type,type,
contract: $i ).
thf(ap_contractE_c2_type,type,
ap_contractE_c2: $i > $i > $i > $o ).
thf(combS_type,type,
combS: $i ).
thf(ap_contractE_sk1p_type,type,
ap_contractE_sk1p: $i > $i > $i > $i ).
thf(ap_contractE_sk1q_type,type,
ap_contractE_sk1q: $i > $i > $i > $i ).
thf(ap_parcontractE_c1_type,type,
ap_parcontractE_c1: $i > $i > $i > $o ).
thf(ap_parcontractE_c2_type,type,
ap_parcontractE_c2: $i > $i > $i > $o ).
thf(ap_parcontractE_c3_type,type,
ap_parcontractE_c3: $i > $i > $i > $o ).
thf(ap_parcontractE_sk1q_type,type,
ap_parcontractE_sk1q: $i > $i > $i > $i ).
thf(ap_parcontractE_sk1p_type,type,
ap_parcontractE_sk1p: $i > $i > $i > $i ).
thf(rtrancl_type,type,
rtrancl: $i > $i ).
thf(ap_parcontractE_sk2q_type,type,
ap_parcontractE_sk2q: $i > $i > $i > $i ).
thf(ap_contractE_c1_type,type,
ap_contractE_c1: $i > $i > $i > $o ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ A ) @ parcontract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros2) ).
thf(115,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ A ) @ parcontract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(55,axiom,
member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ parcontract,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_parcontractD_h1) ).
thf(184,plain,
member @ ( pair @ ( comb_app @ combK @ p ) @ r ) @ parcontract,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ A @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E1) ).
thf(152,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ A @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( member @ ( pair @ combK @ A ) @ parcontract )
| ( member @ combK @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_parcontractE1) ).
thf(137,plain,
! [A: $i] :
( ~ ( member @ ( pair @ combK @ A ) @ parcontract )
| ( member @ combK @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c2 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE5) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c2 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( comb_app @ A @ B ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros3) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( comb_app @ A @ B ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE11) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( C
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ A @ B @ C ) @ B ) @ ( comb_app @ ( ap_parcontractE_sk1q @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE10) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( C
= ( comb_app @ ( comb_app @ ( ap_parcontractE_sk1p @ A @ B @ C ) @ B ) @ ( comb_app @ ( ap_parcontractE_sk1q @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( comb_app @ A @ B ) @ C ) @ parcontract )
| ( ap_parcontractE_c1 @ A @ B @ C )
| ( ap_parcontractE_c2 @ A @ B @ C )
| ( ap_parcontractE_c3 @ A @ B @ C )
| ( ap_parcontractE_c4 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE1) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( comb_app @ A @ B ) @ C ) @ parcontract )
| ( ap_parcontractE_c1 @ A @ B @ C )
| ( ap_parcontractE_c2 @ A @ B @ C )
| ( ap_parcontractE_c3 @ A @ B @ C )
| ( ap_parcontractE_c4 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE3) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( A
= ( comb_app @ combK @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE4) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( A
= ( comb_app @ combK @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c1 @ A @ B @ C )
| ( C
= ( comb_app @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE3) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c1 @ A @ B @ C )
| ( C
= ( comb_app @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( C
= ( comb_app @ ( ap_contractE_sk2q @ A @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE12) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( C
= ( comb_app @ ( ap_contractE_sk2q @ A @ B @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) ) @ parcontract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros3) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) ) @ parcontract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( r
!= ( comb_app @ combK @ A ) )
| ~ ( member @ ( pair @ p @ A ) @ parcontract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_parcontractD_c1) ).
thf(56,plain,
! [A: $i] :
( ( r
!= ( comb_app @ combK @ A ) )
| ~ ( member @ ( pair @ p @ A ) @ parcontract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( combK
!= ( comb_app @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
thf(142,plain,
! [B: $i,A: $i] :
( combK
!= ( comb_app @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(53,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
thf(179,plain,
combK != combS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c2 @ A @ B @ C )
| ( A
= ( comb_app @ combK @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE6) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c2 @ A @ B @ C )
| ( A
= ( comb_app @ combK @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( C
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ A @ B @ C ) @ B ) @ ( comb_app @ ( ap_contractE_sk1q @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE8) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( C
= ( comb_app @ ( comb_app @ ( ap_contractE_sk1p @ A @ B @ C ) @ B ) @ ( comb_app @ ( ap_contractE_sk1q @ A @ B @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c2 @ A @ B @ C )
| ( member @ C @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE4) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c2 @ A @ B @ C )
| ( member @ C @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( comb_app @ A @ C )
= ( comb_app @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app3) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( C != D )
| ( ( comb_app @ A @ C )
= ( comb_app @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( C
= ( comb_app @ A @ ( ap_contractE_sk3q @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE15) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( C
= ( comb_app @ A @ ( ap_contractE_sk3q @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( A
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ A @ B @ C ) ) @ ( ap_contractE_sk1q @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE9) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( A
= ( comb_app @ ( comb_app @ combS @ ( ap_contractE_sk1p @ A @ B @ C ) ) @ ( ap_contractE_sk1q @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app2) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c4 @ A @ B @ C )
| ( member @ ( pair @ A @ ( ap_parcontractE_sk2q @ A @ B @ C ) ) @ parcontract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE12) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c4 @ A @ B @ C )
| ( member @ ( pair @ A @ ( ap_parcontractE_sk2q @ A @ B @ C ) ) @ parcontract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( member @ ( ap_parcontractE_sk1p @ A @ B @ C ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE7) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( member @ ( ap_parcontractE_sk1p @ A @ B @ C ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c4 @ A @ B @ C )
| ( member @ ( pair @ B @ ( ap_parcontractE_sk2s @ A @ B @ C ) ) @ parcontract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE13) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c4 @ A @ B @ C )
| ( member @ ( pair @ B @ ( ap_parcontractE_sk2s @ A @ B @ C ) ) @ parcontract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1q @ A @ B @ C ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE6) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1q @ A @ B @ C ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( combS
!= ( comb_app @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
thf(124,plain,
! [B: $i,A: $i] :
( combS
!= ( comb_app @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i] :
~ ( member @ ( pair @ combK @ A ) @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_contractE) ).
thf(77,plain,
! [A: $i] :
~ ( member @ ( pair @ combK @ A ) @ contract ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE9) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ C @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE2) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c1 @ A @ B @ C )
| ( member @ C @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c4 @ A @ B @ C )
| ( C
= ( comb_app @ ( ap_parcontractE_sk2q @ A @ B @ C ) @ ( ap_parcontractE_sk2s @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE14) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c4 @ A @ B @ C )
| ( C
= ( comb_app @ ( ap_parcontractE_sk2q @ A @ B @ C ) @ ( ap_parcontractE_sk2s @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E2) ).
thf(166,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( comb_app @ A @ B ) @ comb )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1p @ A @ B @ C ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE5) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ ( ap_contractE_sk1p @ A @ B @ C ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ A ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contract_K) ).
thf(161,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ combK @ A ) @ B ) @ A ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( member @ ( ap_parcontractE_sk1q @ A @ B @ C ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE8) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( member @ ( ap_parcontractE_sk1q @ A @ B @ C ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ A @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE14) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ A @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( member @ ( pair @ combS @ A ) @ parcontract )
| ( A = combS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_parcontractE2) ).
thf(81,plain,
! [A: $i] :
( ~ ( member @ ( pair @ combS @ A ) @ parcontract )
| ( A = combS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduction_refl) ).
thf(98,plain,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ ( rtrancl @ contract ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ parcontract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros1) ).
thf(67,plain,
! [A: $i] :
( ~ ( member @ A @ comb )
| ( member @ ( pair @ A @ A ) @ parcontract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ parcontract )
| ~ ( member @ ( pair @ C @ D ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ A @ C ) @ ( comb_app @ B @ D ) ) @ parcontract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros4) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ A @ B ) @ parcontract )
| ~ ( member @ ( pair @ C @ D ) @ parcontract )
| ( member @ ( pair @ ( comb_app @ A @ C ) @ ( comb_app @ B @ D ) ) @ parcontract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( comb_app @ A @ B ) @ C ) @ contract )
| ( ap_contractE_c1 @ A @ B @ C )
| ( ap_contractE_c2 @ A @ B @ C )
| ( ap_contractE_c3 @ A @ B @ C )
| ( ap_contractE_c4 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE1) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( pair @ ( comb_app @ A @ B ) @ C ) @ contract )
| ( ap_contractE_c1 @ A @ B @ C )
| ( ap_contractE_c2 @ A @ B @ C )
| ( ap_contractE_c3 @ A @ B @ C )
| ( ap_contractE_c4 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(42,axiom,
! [A: $i] :
~ ( member @ ( pair @ combS @ A ) @ contract ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_contractE) ).
thf(154,plain,
! [A: $i] :
~ ( member @ ( pair @ combS @ A ) @ contract ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ ( pair @ B @ ( ap_contractE_sk3q @ A @ B @ C ) ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE13) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c4 @ A @ B @ C )
| ( member @ ( pair @ B @ ( ap_contractE_sk3q @ A @ B @ C ) ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app1) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( comb_app @ A @ B )
!= ( comb_app @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(44,axiom,
member @ combK @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros1) ).
thf(158,plain,
member @ combK @ comb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
member @ combS @ comb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros2) ).
thf(114,plain,
member @ combS @ comb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ B @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE7) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c2 @ A @ B @ C )
| ( member @ B @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( A
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ A @ B @ C ) ) @ ( ap_parcontractE_sk1q @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE11) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c3 @ A @ B @ C )
| ( A
= ( comb_app @ ( comb_app @ combS @ ( ap_parcontractE_sk1p @ A @ B @ C ) ) @ ( ap_parcontractE_sk1q @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c1 @ A @ B @ C )
| ( member @ ( comb_app @ A @ B ) @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE2) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_parcontractE_c1 @ A @ B @ C )
| ( member @ ( comb_app @ A @ B ) @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contract_S) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ comb )
| ~ ( member @ B @ comb )
| ~ ( member @ C @ comb )
| ( member @ ( pair @ ( comb_app @ ( comb_app @ ( comb_app @ combS @ A ) @ B ) @ C ) @ ( comb_app @ ( comb_app @ A @ C ) @ ( comb_app @ B @ C ) ) ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ ( pair @ A @ ( ap_contractE_sk2q @ A @ B @ C ) ) @ contract ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE10) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ap_contractE_c3 @ A @ B @ C )
| ( member @ ( pair @ A @ ( ap_contractE_sk2q @ A @ B @ C ) ) @ contract ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( member @ ( pair @ combS @ A ) @ parcontract )
| ( member @ combS @ comb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_parcontractE1) ).
thf(90,plain,
! [A: $i] :
( ~ ( member @ ( pair @ combS @ A ) @ parcontract )
| ( member @ combS @ comb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( member @ ( pair @ combK @ A ) @ parcontract )
| ( A = combK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_parcontractE2) ).
thf(111,plain,
! [A: $i] :
( ~ ( member @ ( pair @ combK @ A ) @ parcontract )
| ( A = combK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(185,plain,
$false,
inference(cvc4,[status(thm)],[115,184,152,137,156,59,135,145,150,104,168,163,69,88,56,142,179,106,121,84,61,132,74,117,102,92,65,109,124,77,96,173,129,166,148,161,86,159,81,98,67,182,127,154,72,175,158,114,171,139,79,94,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL092-1 : TPTP v8.1.2. Released v2.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 14:05:08 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.10/1.02 % [INFO] Parsing done (145ms).
% 1.10/1.03 % [INFO] Running in sequential loop mode.
% 1.89/1.25 % [INFO] eprover registered as external prover.
% 1.89/1.25 % [INFO] cvc4 registered as external prover.
% 1.89/1.26 % [INFO] Scanning for conjecture ...
% 2.11/1.34 % [INFO] Found a conjecture and 54 axioms. Running axiom selection ...
% 2.25/1.40 % [INFO] Axiom selection finished. Selected 54 axioms (removed 0 axioms).
% 2.25/1.45 % [INFO] Problem is propositional (TPTP CNF).
% 2.25/1.45 % [INFO] Type checking passed.
% 2.25/1.46 % [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 ...
% 4.24/2.08 % External prover 'cvc4' found a proof!
% 4.24/2.08 % [INFO] Killing All external provers ...
% 4.24/2.08 % Time passed: 1546ms (effective reasoning time: 1048ms)
% 4.24/2.08 % 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)>
% 4.24/2.08 % Axioms used in derivation (54): comb_intros3, ap_parcontractE10, parcontract_intros2, ap_parcontractE7, ap_contractE4, ap_contractE11, k1_parcontractD_h1, parcontract_intros4, s_parcontractE1, ap_contractE9, ap_parcontractE13, ap_contractE7, ap_parcontractE14, ap_contractE10, app_app3, ap_parcontractE3, parcontract_intros3, ap_contractE2, k_parcontractE1, ap_contractE14, ap_parcontractE6, app_app2, s_app, k_s, ap_parcontractE1, ap_E1, k_contractE, ap_parcontractE11, ap_contractE15, ap_contractE1, ap_contractE8, s_parcontractE2, contract_K, app_app1, ap_parcontractE5, s_contractE, reduction_refl, ap_contractE12, ap_parcontractE2, ap_contractE5, ap_E2, comb_intros1, ap_parcontractE12, k_app, ap_parcontractE9, parcontract_intros1, contract_S, comb_intros2, ap_contractE6, ap_parcontractE4, ap_contractE13, k_parcontractE2, ap_parcontractE8, ap_contractE3
% 4.24/2.08 % No. of inferences in proof: 111
% 4.24/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1546 ms resp. 1048 ms w/o parsing
% 4.43/2.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.43/2.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------