TSTP Solution File: COL077-1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL077-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:29:29 EDT 2024
% Result : Unsatisfiable 63.04s 11.07s
% Output : Refutation 63.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 109 ( 49 unt; 9 typ; 0 def)
% Number of atoms : 164 ( 163 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 868 ( 114 ~; 64 |; 0 &; 690 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 126 ( 0 ^ 126 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(apply_type,type,
apply: $i > $i > $i ).
thf(abstraction_type,type,
abstraction: $i ).
thf(identity_type,type,
identity: $i ).
thf(k_type,type,
k: $i > $i ).
thf(projection1_type,type,
projection1: $i ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(projection2_type,type,
projection2: $i ).
thf(eq_type,type,
eq: $i ).
thf(n_type,type,
n: $i > $i > $i ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( apply @ ( k @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( apply @ ( k @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( apply @ ( k @ A ) @ B )
= A ),
inference(lifteq,[status(thm)],[16]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ ( k @ C ) ) @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ ( k @ C ) ) @ ( apply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ ( k @ C ) ) @ ( apply @ B @ C ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(1,negated_conjecture,
( ( apply @ ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction )
!= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1a) ).
thf(13,plain,
( ( apply @ ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction )
!= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,plain,
( ( apply @ ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction )
!= identity ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( apply @ ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction )
!= identity ),
inference(lifteq,[status(thm)],[14]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( A != identity )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(133,plain,
! [A: $i] :
( ( ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction )
!= ( k @ identity ) )
| ( A != abstraction ) ),
inference(simp,[status(thm)],[119]) ).
thf(149,plain,
( ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction )
!= ( k @ identity ) ),
inference(simp,[status(thm)],[133]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( A
!= ( k @ identity ) )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[17,149]) ).
thf(284,plain,
! [A: $i] :
( ( ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction )
!= ( k @ ( k @ identity ) ) )
| ( A != abstraction ) ),
inference(simp,[status(thm)],[263]) ).
thf(296,plain,
( ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction )
!= ( k @ ( k @ identity ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( ( ( apply @ ( apply @ A @ ( k @ C ) ) @ ( apply @ B @ C ) )
!= ( k @ ( k @ identity ) ) )
| ( ( apply @ ( apply @ ( apply @ abstraction @ A ) @ B ) @ C )
!= ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[27,296]) ).
thf(888,plain,
( ( apply @ ( apply @ abstraction @ ( k @ abstraction ) ) @ ( apply @ abstraction @ abstraction ) )
!= ( k @ ( k @ identity ) ) ),
inference(pattern_uni,[status(thm)],[887:[bind(A,$thf( abstraction )),bind(B,$thf( abstraction )),bind(C,$thf( abstraction ))]]) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( A
!= ( k @ ( k @ identity ) ) )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ ( apply @ abstraction @ ( k @ abstraction ) ) @ ( apply @ abstraction @ abstraction ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,888]) ).
thf(1160,plain,
! [A: $i] :
( ( ( apply @ abstraction @ ( k @ abstraction ) )
!= ( k @ ( k @ ( k @ identity ) ) ) )
| ( A
!= ( apply @ abstraction @ abstraction ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1168,plain,
( ( apply @ abstraction @ ( k @ abstraction ) )
!= ( k @ ( k @ ( k @ identity ) ) ) ),
inference(simp,[status(thm)],[1160]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( pair @ A @ B ) @ C )
= ( pair @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( pair @ A @ B ) @ C )
= ( pair @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( pair @ ( apply @ A @ C ) @ ( apply @ B @ C ) )
= ( apply @ ( pair @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(8,axiom,
! [A: $i] :
( ( apply @ eq @ ( pair @ A @ A ) )
= projection1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).
thf(28,plain,
! [A: $i] :
( ( apply @ eq @ ( pair @ A @ A ) )
= projection1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,plain,
! [A: $i] :
( ( apply @ eq @ ( pair @ A @ A ) )
= projection1 ),
inference(lifteq,[status(thm)],[28]) ).
thf(538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( apply @ eq @ ( apply @ ( pair @ A @ B ) @ C ) )
= projection1 )
| ( ( pair @ ( apply @ A @ C ) @ ( apply @ B @ C ) )
!= ( pair @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25,29]) ).
thf(539,plain,
! [B: $i,A: $i] :
( ( apply @ eq @ ( apply @ ( pair @ A @ A ) @ B ) )
= projection1 ),
inference(pattern_uni,[status(thm)],[538:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( apply @ B @ F ))]]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( apply @ eq @ ( apply @ ( pair @ A @ A ) @ B ) )
= projection1 ),
inference(simp,[status(thm)],[539]) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( apply @ ( apply @ ( apply @ A @ ( k @ C ) ) @ ( apply @ B @ C ) ) @ abstraction )
!= ( k @ identity ) )
| ( ( apply @ ( apply @ ( apply @ abstraction @ A ) @ B ) @ C )
!= ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[27,149]) ).
thf(905,plain,
( ( apply @ ( apply @ ( apply @ abstraction @ ( k @ abstraction ) ) @ ( apply @ abstraction @ abstraction ) ) @ abstraction )
!= ( k @ identity ) ),
inference(pattern_uni,[status(thm)],[904:[bind(A,$thf( abstraction )),bind(B,$thf( abstraction )),bind(C,$thf( abstraction ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( pair @ ( apply @ projection1 @ A ) @ ( apply @ projection2 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairing) ).
thf(22,plain,
! [A: $i] :
( ( pair @ ( apply @ projection1 @ A ) @ ( apply @ projection2 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
! [A: $i] :
( ( pair @ ( apply @ projection1 @ A ) @ ( apply @ projection2 @ A ) )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ eq @ ( pair @ A @ B ) )
= projection2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ eq @ ( pair @ A @ B ) )
= projection2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ eq @ ( pair @ A @ B ) )
= projection2 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ eq @ ( pair @ A @ B ) )
= projection2 ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(496,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( apply @ eq @ A )
= projection2 )
| ( ( pair @ ( apply @ projection1 @ A ) @ ( apply @ projection2 @ A ) )
!= ( pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,32]) ).
thf(497,plain,
! [A: $i] :
( ( ( apply @ projection2 @ A )
= ( apply @ projection1 @ A ) )
| ( ( apply @ eq @ A )
= projection2 ) ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( G )),bind(B,$thf( apply @ projection1 @ G )),bind(C,$thf( apply @ projection2 @ G ))]]) ).
thf(534,plain,
! [A: $i] :
( ( ( apply @ projection2 @ A )
= ( apply @ projection1 @ A ) )
| ( ( apply @ eq @ A )
= projection2 ) ),
inference(simp,[status(thm)],[497]) ).
thf(705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( apply @ eq @ ( apply @ ( apply @ ( pair @ A @ B ) @ C ) @ E ) )
= projection1 )
| ( ( pair @ ( apply @ A @ C ) @ ( apply @ B @ C ) )
!= ( pair @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25,582]) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ eq @ ( apply @ ( apply @ ( pair @ A @ A ) @ C ) @ B ) )
= projection1 ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( apply @ B @ G )),bind(E,$thf( E ))]]) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ eq @ ( apply @ ( apply @ ( pair @ A @ A ) @ C ) @ B ) )
= projection1 ),
inference(simp,[status(thm)],[706]) ).
thf(12,axiom,
! [A: $i] :
( ( apply @ identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
thf(39,plain,
! [A: $i] :
( ( apply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(40,plain,
! [A: $i] :
( ( apply @ identity @ A )
= A ),
inference(lifteq,[status(thm)],[39]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( A
!= ( k @ ( k @ identity ) ) )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[17,296]) ).
thf(322,plain,
! [A: $i] :
( ( ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction )
!= ( k @ ( k @ ( k @ identity ) ) ) )
| ( A != abstraction ) ),
inference(simp,[status(thm)],[305]) ).
thf(327,plain,
( ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction )
!= ( k @ ( k @ ( k @ identity ) ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(336,plain,
! [A: $i] :
( ( A
!= ( k @ ( k @ ( k @ identity ) ) ) )
| ( ( apply @ identity @ A )
!= ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[40,327]) ).
thf(350,plain,
( ( ( apply @ abstraction @ abstraction )
!= identity )
| ( ( k @ ( k @ ( k @ identity ) ) )
!= abstraction ) ),
inference(simp,[status(thm)],[336]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ A @ ( n @ A @ B ) )
!= ( apply @ B @ ( n @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ A @ ( n @ A @ B ) )
!= ( apply @ B @ ( n @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ A @ ( n @ A @ B ) )
!= ( apply @ B @ ( n @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( apply @ A @ ( n @ A @ B ) )
!= ( apply @ B @ ( n @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( apply @ ( apply @ ( apply @ ( apply @ A @ ( k @ C ) ) @ ( apply @ B @ C ) ) @ abstraction ) @ abstraction )
!= identity )
| ( ( apply @ ( apply @ ( apply @ abstraction @ A ) @ B ) @ C )
!= ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(859,plain,
( ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ ( k @ abstraction ) ) @ ( apply @ abstraction @ abstraction ) ) @ abstraction ) @ abstraction )
!= identity ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( abstraction )),bind(B,$thf( abstraction )),bind(C,$thf( abstraction ))]]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( A
!= ( k @ ( k @ ( k @ identity ) ) ) )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[17,327]) ).
thf(348,plain,
! [A: $i] :
( ( ( apply @ abstraction @ abstraction )
!= ( k @ ( k @ ( k @ ( k @ identity ) ) ) ) )
| ( A != abstraction ) ),
inference(simp,[status(thm)],[338]) ).
thf(358,plain,
( ( apply @ abstraction @ abstraction )
!= ( k @ ( k @ ( k @ ( k @ identity ) ) ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( A
!= ( k @ ( k @ ( k @ ( k @ identity ) ) ) ) )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ abstraction @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[17,358]) ).
thf(461,plain,
! [A: $i] :
( ( ( k @ ( k @ ( k @ ( k @ ( k @ identity ) ) ) ) )
!= abstraction )
| ( A != abstraction ) ),
inference(simp,[status(thm)],[450]) ).
thf(465,plain,
( ( k @ ( k @ ( k @ ( k @ ( k @ identity ) ) ) ) )
!= abstraction ),
inference(simp,[status(thm)],[461]) ).
thf(681,plain,
! [B: $i,A: $i] :
( ( A != identity )
| ( ( k @ ( k @ ( k @ identity ) ) )
!= abstraction )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ abstraction @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[17,350]) ).
thf(692,plain,
! [A: $i] :
( ( ( k @ ( k @ ( k @ identity ) ) )
!= abstraction )
| ( ( k @ identity )
!= abstraction )
| ( A != abstraction ) ),
inference(simp,[status(thm)],[681]) ).
thf(699,plain,
( ( ( k @ ( k @ ( k @ identity ) ) )
!= abstraction )
| ( ( k @ identity )
!= abstraction ) ),
inference(simp,[status(thm)],[692]) ).
thf(799,plain,
( ( ( k @ identity )
!= abstraction )
| ( ( k @ ( k @ ( k @ identity ) ) )
!= ( k @ identity ) )
| ( abstraction != abstraction ) ),
inference(eqfactor_ordered,[status(thm)],[699]) ).
thf(800,plain,
( ( ( k @ identity )
!= abstraction )
| ( ( k @ ( k @ ( k @ identity ) ) )
!= ( k @ identity ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( apply @ projection2 @ ( pair @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( apply @ projection2 @ ( pair @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( apply @ projection2 @ ( pair @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[20]) ).
thf(11,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_projections) ).
thf(36,plain,
projection1 != projection2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,plain,
projection1 != projection2,
inference(polarity_switch,[status(thm)],[36]) ).
thf(38,plain,
projection2 != projection1,
inference(lifteq,[status(thm)],[37]) ).
thf(537,plain,
! [A: $i] :
( ( apply @ ( pair @ projection1 @ projection2 ) @ A )
= A ),
inference(rewrite,[status(thm)],[23,25]) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( A
!= ( k @ ( k @ ( k @ identity ) ) ) )
| ( ( apply @ ( k @ A ) @ B )
!= ( apply @ abstraction @ ( k @ abstraction ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,1168]) ).
thf(1202,plain,
! [A: $i] :
( ( ( k @ ( k @ ( k @ ( k @ identity ) ) ) )
!= abstraction )
| ( A
!= ( k @ abstraction ) ) ),
inference(simp,[status(thm)],[1185]) ).
thf(1207,plain,
( ( k @ ( k @ ( k @ ( k @ identity ) ) ) )
!= abstraction ),
inference(simp,[status(thm)],[1202]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( apply @ projection1 @ ( pair @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection1) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( apply @ projection1 @ ( pair @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(50,plain,
! [A: $i] :
( ( A != identity )
| ( ( apply @ identity @ A )
!= ( apply @ ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[40,15]) ).
thf(62,plain,
( ( ( apply @ ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) @ abstraction )
!= identity )
| ( identity != abstraction ) ),
inference(simp,[status(thm)],[50]) ).
thf(78,plain,
! [A: $i] :
( ( ( apply @ ( apply @ ( apply @ A @ abstraction ) @ abstraction ) @ abstraction )
!= identity )
| ( identity != abstraction )
| ( ( apply @ identity @ A )
!= ( apply @ abstraction @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[40,62]) ).
thf(80,plain,
! [A: $i] :
( ( ( apply @ ( apply @ ( apply @ A @ abstraction ) @ abstraction ) @ abstraction )
!= identity )
| ( identity != abstraction )
| ( identity != abstraction )
| ( A != abstraction ) ),
inference(simp,[status(thm)],[78]) ).
thf(89,plain,
( ( ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction )
!= identity )
| ( identity != abstraction ) ),
inference(simp,[status(thm)],[80]) ).
thf(96,plain,
! [A: $i] :
( ( A != identity )
| ( identity != abstraction )
| ( ( apply @ identity @ A )
!= ( apply @ ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[40,89]) ).
thf(102,plain,
( ( identity != abstraction )
| ( ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction )
!= identity )
| ( identity != abstraction ) ),
inference(simp,[status(thm)],[96]) ).
thf(107,plain,
( ( identity != abstraction )
| ( ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction )
!= identity ) ),
inference(simp,[status(thm)],[102]) ).
thf(167,plain,
! [A: $i] :
( ( identity != abstraction )
| ( A != identity )
| ( ( apply @ identity @ A )
!= ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[40,107]) ).
thf(174,plain,
( ( identity != abstraction )
| ( ( apply @ abstraction @ abstraction )
!= identity )
| ( identity != abstraction ) ),
inference(simp,[status(thm)],[167]) ).
thf(180,plain,
( ( identity != abstraction )
| ( ( apply @ abstraction @ abstraction )
!= identity ) ),
inference(simp,[status(thm)],[174]) ).
thf(183,plain,
! [A: $i] :
( ( identity != abstraction )
| ( A != identity )
| ( ( apply @ identity @ A )
!= ( apply @ abstraction @ abstraction ) ) ),
inference(paramod_ordered,[status(thm)],[40,180]) ).
thf(187,plain,
( ( identity != abstraction )
| ( identity != abstraction )
| ( identity != abstraction ) ),
inference(simp,[status(thm)],[183]) ).
thf(190,plain,
identity != abstraction,
inference(simp,[status(thm)],[187]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( apply @ projection1 @ ( pair @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(801,plain,
( ( ( k @ identity )
!= abstraction )
| ( ( k @ ( k @ identity ) )
!= identity ) ),
inference(simp,[status(thm)],[799]) ).
thf(30525,plain,
$false,
inference(e,[status(thm)],[1168,582,905,534,783,13,888,350,39,35,16,859,465,800,15,24,25,20,29,21,33,28,38,537,1207,32,296,17,149,22,27,18,327,699,40,26,36,30,190,19,801,358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL077-1 : TPTP v8.1.2. Released v1.2.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:04:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (125ms).
% 1.22/1.01 % [INFO] Running in sequential loop mode.
% 1.66/1.23 % [INFO] eprover registered as external prover.
% 1.66/1.23 % [INFO] cvc4 registered as external prover.
% 1.66/1.23 % [INFO] Scanning for conjecture ...
% 1.86/1.28 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.86/1.30 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.02/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 2.02/1.32 % [INFO] Type checking passed.
% 2.02/1.33 % [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 ...
% 63.04/11.07 % External prover 'e' found a proof!
% 63.04/11.07 % [INFO] Killing All external provers ...
% 63.04/11.07 % Time passed: 10539ms (effective reasoning time: 10060ms)
% 63.04/11.07 % 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)>
% 63.04/11.07 % Axioms used in derivation (11): abstraction, k_definition, pairwise_application, extensionality2, projection2, different_projections, pairing, projection1, identity_definition, equality, extensionality1
% 63.04/11.07 % No. of inferences in proof: 100
% 63.04/11.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10539 ms resp. 10060 ms w/o parsing
% 63.04/11.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.04/11.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------